Multiscale modelling of industrial flighted rotary dryers · Title: Multiscale modelling of industrial flighted rotary dryers Author: Olukayode Oludamilola Ajayi Created Date: 12/12/2012

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Ajayi, Olukayode Oludamilola (2011) Multiscale

modelling of industrial flighted rotary dryers. PhD thesis,

James Cook University.

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MULTISCALE MODELLI G OF I DUSTRIAL FLIGHTED ROTARY DRYERS

Thesis submitted by

Olukayode Oludamilola AJAYI, B.Tech(Hons), M.Sc (Eng) UCT

in December 2011

For the degree of Doctor of Philosophy

in the School of Engineering

James Cook University

ii

STATEME T OF ACCESS

I, the undersigned, author of this work, understand that James Cook University will make this

thesis available for use within the University Library and, via the Australian Digital Theses

network, for use elsewhere.

I understand that, as an unpublished work, a thesis has significant protection under the copyright

Act and;

I do not wish to place any further restriction on access to this work.

31st December 2011

Olukayode Ajayi

iii

DECLARATIO

I declare that this thesis is my own work and has not been submitted in any form for another

degree or diploma at any university or other institution of tertiary education. Information derived

from the published or unpublished work of others has been acknowledged in the text and a list of

references is given.

31st December 2011

Olukayode Ajayi

iv

STATEME T O THE CO TRIBUTIO OF OTHERS

The research project was funded by MMG Century mine, Australia. Tuition fee scholarship and

stipend support was received from the School of Engineering and Physical Sciences. Graduate

research scholarship awards were used to purchase high performance workstation and licenses

for gProms and CFX softwares.

Inductively coupled plasma mass spectrometry (ICP-MS) and X-ray diffraction analysis was

undertaken at James Cook University Advanced Analytical Center. Wendy Smith provided

assistance with the editing of the final thesis.

v

ACK OWLEDGEME TS

I express my unreserved gratitude to God for His love, faithfulness and wisdom throughout the

research. This piece of work is dedicated to Him.

I am deeply indebted to my supervisor Dr Madoc Sheehan for his unwavering support and

guidance throughout the research. Thanks to MMG operation team leaders Scott Findlay and

Clyde Goody for their support during the industrial experiments.

Many thanks to my fellow graduate students, Shaun, Reza, Om, Manish, Sepideh, Dhanya, Rhys,

Raymond Kazum and Hassan for their stimulating discussions during the course of study. I am

grateful to my friends Danielle, Lolade, Oyebola, Adams, Kofi and Abena for their constant

encouragement.

Special thanks to my siblings Omotuyole, Busayo and Femi for their love and support. Thanks to

my wife’s mum for her moral support and inspiring words. I express my sincere gratitude to my

parents for their continuous support, prayers and for believing in my dreams and career path.

My deepest expression of appreciation goes to my wife and son, Olubunmi Asake and David for

their understanding, love, support and prayers. Thanks for your encouragement during the tough

times of this research and for bearing my long working hours.

Thanks to everyone who has contributed to the success of this research one-way or the other.

vi

TABLE OF CO TE T

STATEME T OF ACCESS ....................................................................................................... II

DECLARATIO ......................................................................................................................... III

STATEME T O THE CO TRIBUTIO OF OTHERS .................................................... IV

ACK OWLEDGEME TS ........................................................................................................ V

TABLE OF CO TE T .............................................................................................................. VI

LIST OF FIGURES .................................................................................................................. XII

LIST OF TABLES ................................................................................................................. XVII

OME CLATURE ....................................................................................................................... I

ABSTRACT ................................................................................................................................... 1

1. I TRODUCTIO ................................................................................................................. 1

1.1 Motivation .......................................................................................................................... 2

1.2 Objectives and aim ............................................................................................................ 5

1.3 Structure of thesis ............................................................................................................. 5

2. LITERATURE REVIEW .................................................................................................... 8

2.1 Holdup ................................................................................................................................ 8

2.1.1 Design load ..................................................................................................................... 9

2.2 Residence time ................................................................................................................. 13

2.3 Modelling approaches ..................................................................................................... 15

2.3.1 Unflighted dryer ............................................................................................................ 16

2.3.2 Flighted rotary dryers .................................................................................................... 17

2.4 Summary .......................................................................................................................... 20

3. I DUSTRIAL SCALE TESTI G .................................................................................... 22

vii

3.1 Process description.......................................................................................................... 23

3.2 Geometrical Configuration of the industrial dryer ..................................................... 24

3.3 Characterisation of the combustion chamber .............................................................. 26

3.4 Physical properties of zinc concentrates ....................................................................... 26

3.4.1 Moisture content profile ................................................................................................ 26

3.4.2 Dynamic angle of repose .............................................................................................. 27

3.4.3 Particle size ................................................................................................................... 30

3.4.4 Bulk density .................................................................................................................. 31

3.5 Residence Time Distribution (RTD) Tests .................................................................... 32

3.5.1 Experimental studies ..................................................................................................... 32

3.5.2 RTD test methodology .................................................................................................. 33

3.5.2.1 Tracer standard solution approach (Test 1) .......................................................... 34

3.5.2.2 Solid tracer pre-mixed with inlet solid (Test 2) .................................................... 34

3.5.3 Data analysis ................................................................................................................. 36

3.5.4 RTD operational conditions .......................................................................................... 38

3.5.4.1 Hold-up ................................................................................................................. 43

3.6 Shell temperature measurement .................................................................................... 43

4. DESIG LOADI G I FLIGHTED ROTARY DRYERS ............................................ 45

4.1 Experimental set-up ........................................................................................................ 49

4.1.1 Material and its properties ............................................................................................ 51

4.2 Image segmentation and manual analysis .................................................................... 52

4.2.1 Image enhancement ...................................................................................................... 54

4.2.1.1 Filtering and thresholding in ImageJ software...................................................... 56

viii

4.3 Validation of image analysis .......................................................................................... 58

4.4 Estimation of design load ............................................................................................... 59

4.4.1 Visual analysis approach............................................................................................... 60

4.4.2 Change in gradient of total flight-borne solids ............................................................. 61

4.4.3 Saturation of the airborne solids and of the flight-borne solids in the upper half of the

drum …………………………………………………………………………………………62

4.4.4 Saturation of the First Unloading Flight (FUF) ............................................................ 63

4.5 Estimation of the airborne solids ................................................................................... 68

4.5.1 Vessel geometry and grid generation ............................................................................ 73

4.5.2 Boundary conditions ..................................................................................................... 76

4.5.3 Simulation ..................................................................................................................... 76

4.5.4 Results and Discussion ................................................................................................. 77

4.6 Application of geometric modelling to predict design loading ................................... 83

4.7 Summary .......................................................................................................................... 88

5. SOLID TRA SPORT MODELLI G .............................................................................. 90

5.1 Model development ......................................................................................................... 90

5.1.1 Flighted section ............................................................................................................. 92

5.1.2 Unflighted section ......................................................................................................... 94

5.1.3 Boundary conditions ..................................................................................................... 95

5.2 Model parameters ........................................................................................................... 96

5.2.1 Geometric modelling .................................................................................................... 98

5.2.2 Flighted section ........................................................................................................... 100

5.2.3 Unflighted section ....................................................................................................... 102

ix

5.2.4 Scaling effects ............................................................................................................. 102

5.3 Multi-scale model architecture .................................................................................... 104

5.3.1 Numerical solution and parameter estimation ............................................................ 105

5.4 Model results ................................................................................................................. 110

5.4.1 Model sensitivity ......................................................................................................... 116

5.4.1.1 Effect of internal diameter .................................................................................. 116

5.4.1.2 Effect of rotational speed .................................................................................... 119

5.5 Summary ........................................................................................................................ 121

6. MATHEMATICAL MODELLI G OF A I DUSTRIAL FLIGHTED ROTARY

DRYER ...................................................................................................................................... 122

6.1 Model development ....................................................................................................... 122

6.1.1 Model structure ........................................................................................................... 122

6.1.1.1 Reference states .................................................................................................. 123

6.1.1.2 Flighted section ................................................................................................... 123

6.1.1.3 Unflighted section ............................................................................................... 127

6.1.1.4 Drying rate .......................................................................................................... 133

6.1.1.5 Heat and mass transfer ........................................................................................ 135

6.1.1.6 Heat loss .............................................................................................................. 139

6.1.1.7 Surface area consideration .................................................................................. 141

6.2 Model solution ............................................................................................................... 145

6.2.1 Parameter estimation ................................................................................................... 146

6.3 Model verification ......................................................................................................... 149

6.4 Summary ........................................................................................................................ 153

x

7. MODEL APPLICATIO ................................................................................................ 154

7.1 Relative indices analysis ............................................................................................... 156

7.1.1 Discussion ................................................................................................................... 160

7.2 Optimising fuel consumption ....................................................................................... 162

7.4. Summary ............................................................................................................................. 166

8. CO CLUSIO A D RECOMME DATIO S ............................................................ 168

8.1 Conclusion ..................................................................................................................... 168

8.2 Recommendations ......................................................................................................... 170

REFERE CES .......................................................................................................................... 173

APPE DI CES ........................................................................................................................ 184

APPE DIX A: COMBUSTIO CHAMBER ....................................................................... 184

APPE DIX B: RTD DATA (Lithium concentration as a function of time) ....................... 189

APPE DIX C: MATLAB CODE............................................................................................ 195

APPE DIX D: MATLAB CODE FOR ESTIMATI G DESIG LOAD .......................... 200

APPE DIX E: CO FIDE CE I TERVAL OF DESIG LOAD ..................................... 201

APPE DIX F: gPROMS Code ................................................................................................ 204

Process model ......................................................................................................................... 204

Dryer Model ............................................................................................................................ 214

Air phase ................................................................................................................................. 223

Active phase ............................................................................................................................ 229

Passive phase .......................................................................................................................... 233

Kilning cell for section A ........................................................................................................ 236

Kilning cell for section E ........................................................................................................ 248

xi

Geometric modelling for section B ......................................................................................... 260

Geometric modelling for section C ......................................................................................... 264

Geometric modelling for section D ......................................................................................... 268

Mixing cell .............................................................................................................................. 272

Parameter estimation ............................................................................................................... 275

Experimental entity ................................................................................................................. 276

xii

LIST OF FIGURES

Figure 1.1: Typical example of a co-current rotary dryer ............................................................... 1

Figure 1.2: Cross-section of typical flighted rotary dryer showing the solids cascading ............... 2

Figure 2.1a: Under-loaded dryer (Arrow indicates the 9 o'clock position and demonstrates that

solids are discharged late in the rotation) ............................................................................ 10

Figure 2.1b: Intermediate loading assumed close to design load (Arrow shows there is discharge

at precisely the 9 o'clock position)……………………………………………………………………….10

Figure 2.1c: Overloaded dryer load (Arrow shows there is discharge before 9 o'clock

position)……………………………………………………………………………………………………..11

Figure 2.2: Active and passive phase (Sheehan et al., 2005) ........................................................ 17

Figure 2.3: Model structure........................................................................................................... 18

Figure 3.1: Schematic representation of the MMG combustion chamber and industrial rotary

dryer ...................................................................................................................................... 24

Figure 3.2: Geometrical details of the dryer (All length dimensions are in metres) ..................... 25

Figure 3.3: Moisture content profile along the length of the dryer ............................................... 27

Figure 3.4: Experimental apparatus to measure dynamic angle of repose ................................... 28

Figure 3.5: Dynamic angle of repose versus moisture content ..................................................... 29

Figure 3.6: Mass percentage of the passing (Samples n = 0 to 23 are zinc concentrates samples

that were taken every one meter along the length of the dryer) ........................................... 30

Figure 3.7: Lithium concentration versus time (for method testing RTD trials) .......................... 37

Figure 3.8: Lithium concentration versus time for test runs ......................................................... 41

Figure 3.9: Normalised residence time distribution functions for all tests ................................... 42

Figure 3.10: Shell temperature profile along the length of the dryer ............................................ 44

xiii

Figure 4.1: Algorithm for image analysis ..................................................................................... 48

Figure 4.2: Schematic diagram of the flight geometry ................................................................. 51

Figure 4.3: Drum cross section including the angles used to define the regions of interest for the

Image segmentation. ............................................................................................................. 53

Figure 4.4: Original and filtered images in ImageJ software (upper half filter)........................... 57

Figure 4.5: Plot of holdup against feed rate (Matchett & Baker, 1988) ....................................... 60

Figure 4.6: Total passive (UHD + LHD) versus loading for 0.4 wt% moisture content solids at

3.5 rpm .................................................................................................................................. 61

Figure 4.7: Saturation of the airborne solids and flight-borne solids in the upper half of the drum

(3.5 rpm) ............................................................................................................................... 63

Figure 4.8: Design load of (a) low (0.75 wt% 2.5 rpm, 0.4 wt% (3.5 rpm and 4.5 rpm)), (b)

medium (1.25 wt%) and (c) high (2.1 wt%) moisture content solids at different rotational

speeds .................................................................................................................................... 65

Figure 4.9: Variation in the cropped image pixel intensity for free-flowing and cohesive falling

particle curtains (3.5 rpm) ..................................................................................................... 68

Figure 4.10: The manually traced falling curtains ........................................................................ 69

Figure 4.11: Experimental images of the discharged solid at angular position of 150o ............... 74

Figure 4.12: Geometrically calculated flight discharge mass flow rate profiles at varying

rotational speed ..................................................................................................................... 74

Figure 4.13: Schematic diagram of the CFD model ..................................................................... 76

Figure 4.14: Contour profile of the solid volume fraction ............................................................ 77

Figure 4.15: Area covered by the threshold values within the original image (0.4 wt%, 4.5 rpm)

............................................................................................................................................... 79

xiv

Figure 4.16: Area with CFD contour profiles, which are defined by their solid volume fraction 79

Figure 4.17: Effect of curtain height on solid volume fraction at different mass flow rates (for

free-flowing solids) ............................................................................................................... 81

Figure 4.18: Drum cross section showing the mass averaged falling height geometrical details 87

Figure 5.1: Model structure........................................................................................................... 92

Figure 5.2: Model structure for the flighted section ..................................................................... 93

Figure 5.3: Model structure of the unflighted section characterised by its feed rate (Fs) and length

............................................................................................................................................... 94

Figure 5.4: Drum cross section showing geometrical details (Active cycle time is the time taken

for the solids to fall from point ii to point i while passive cycle time is the time taken for the

discharge particle at point i to move to original discharged point ii). ................................. 97

Figure 5.5: Axial displacement of particle .................................................................................... 97

Figure 5.6: Geometric model structure ....................................................................................... 100

Figure 5.7: Internal radius of a scale accumulated dryer ............................................................ 103

Figure 5.8: Scale accumulation around the flight base (s1) and the flight tip (s2) ...................... 103

Figure 5.9: Interaction between the process model and geometric model .................................. 105

Figure 5.10: Effect of grid size within the unflighted section .................................................... 107

Figure 5.11: RTD profile (Test 2) ............................................................................................... 110





xv

Figure 5.16: Solids distribution within the flighted sections for Test 2 (Holdup in the unflighted

sections: 2237 kg/m) ........................................................................................................... 114


sections: 2044 kg/m) ........................................................................................................... 114


sections: 2593 kg/m) ........................................................................................................... 115


sections: 3039 kg/m) ........................................................................................................... 115


sections: 3024 kg/m) ........................................................................................................... 116

Figure 5.21: Effect of internal diameter and flight loading capacity on RTD ............................ 117

Figure 5.22: Effect of internal diameter on solid distribution (passive) ..................................... 118

Figure 5.23: Effect of internal diameter on solid distribution (active) ....................................... 118

Figure 5.24: Effect of rotational speed on RTD ......................................................................... 120

Figure 5.25: Effect of rotational speed on solid distribution (passive) ....................................... 120

Figure 5.26: Effect of rotational speed on solid distribution (active) ......................................... 121

Figure 6.1: Model structure......................................................................................................... 123

Figure 6.2: Model structure of the flighted section..................................................................... 124

Figure 6.3: Model structure of the unflighted section................................................................. 128

Figure 6.4: Active layer and passive layer in the kilning section (AAL is area of active layer, Akiln

is the chordal area (kilning area)) ...................................................................................... 143

Figure 6.5: Effect of area correction factor on moisture content profile .................................... 148

Figure 6.6: Solid moisture content profile .................................................................................. 149

xvi

Figure 6.7: RTD profile (Test 4) ................................................................................................. 150

Figure 6.8: Solid temperature profile (Test 4) ............................................................................ 151

Figure 6.9: Gas and shell temperature profiles (Test 4) .............................................................. 151

Figure 7.1: Effect of external heat loss on gas temperature profile ............................................ 163

Figure 7.2: Effect of external heat loss on solid temperature profile .......................................... 164

Figure 7.3: Effect of external heat loss on solid outlet moisture content profile ........................ 164

Figure 7.4: Effect of gas inlet temperature on solid moisture content profile in an insulated dryer

............................................................................................................................................. 165

Figure 7.5: Effect of gas inlet temperature on solid temperature profile in an insulated dryer .. 166

xvii

LIST OF TABLES

Table 3.1: List of measurements obtained via sensors ................................................................. 24

Table 3.2: Geometrical configuration of the drum ....................................................................... 25

Table 3.3: Dynamic angle of repose ............................................................................................. 29

Table 3.4: Consolidated bulk densities of the solid ...................................................................... 31

Table 3.5: Operating conditions for Test 1 ................................................................................... 35


Table 3.7: Mass of lithium recovered ........................................................................................... 37



Table 3.10: Operating conditions for Test 5 ................................................................................. 39


Table 3.12: Mass of lithium recovered ......................................................................................... 41

Table 3.13: Moment of RTD ........................................................................................................ 42

Table 3.14: Holdup values for different conditions ...................................................................... 43

Table 4.1: Operating conditions for the design load experiments ................................................ 50

Table 4.2: Experimental set up and geometrical configuration of the drum ................................ 50

Table 4.3: Characteristics of the material at different moisture content ....................................... 52

Table 4.4: Regions of interest corresponding to Figure 4.3 .......................................................... 54

Table 4.5: Comparative estimation of regions of interest (2.5 rpm, 0.4 wt% moisture content, 32

kg loading condition) ............................................................................................................ 55



xviii

Table 4.7: Values for the thresholding process ............................................................................. 57





Table 4.10: Comparative estimation of regions of interest (4.5 rpm, 0.4 wt% moisture content,

34.5kg loading condition) ..................................................................................................... 59

Table 4.11: Design load based on constant area at FUF (at different experimental conditions) .. 66

Table 4.12: Experimental conditions for the 150o free-falling particle curtain ............................ 75

Table 4.13: Threshold value and solid volume fraction ............................................................... 80

Table 4.14: Empirical equations for determining solids volume fraction (αct) within the curtain as

a function of curtain vertical drop distance in cm (hct) (for free-flowing solids) .................. 81

Table 4.15: Active phase for different angles of repose ............................................................... 83

Table 4.16: Percentage of deviation of the design load model ..................................................... 84

Table 4.17: Ratio of airborne to flight-borne solids at design loading (with different angles of

repose)................................................................................................................................... 88

Table 5.1: Number of cells in each flighted section ................................................................... 102

Table 5.2: Estimated parameters for different conditions in the dryer ....................................... 108

Table 5.3: Pearson correlation coefficients between the axial dispersion coefficient and

experimental conditions ...................................................................................................... 108

Table 5.4: Holdup for different operating conditions of the dryer ............................................. 113


Table 6.2: Product moisture content ........................................................................................... 152

xix

Table 6.3: Product temperature ................................................................................................... 152

Table 6.4: Gas outlet temperature ............................................................................................... 153

Table 7.1: Relative indices of output variables for a change in gas inlet temperature ............... 158

Table 7.2: Relative indices of output variables for a change in gas inlet humidity .................... 158

Table 7.3: Relative indices of output variables for a change in rotational speed ....................... 159

Table 7.4: Relative indices of output variables for a change in solid inlet temperature ............ 159

Table 7.5: Relative indices of output variables for a change in solid feed rate .......................... 159

i

OME CLATURE

A area (m2)

Aa slope of the line after break point (Figure E1)

Ab slope of the line before break point (Figure E1)

�� .��.�� ⁄ �m��

ASF percentage covered by scale accumulation (%)

C concentration (ppm)

Ca intercept of the line after break point (Figure E1)

Cb intercept of the line before break point (Figure E1)

CD drag coefficient (-)

��, ��, �� coefficients in turbulence model

CF forward step coefficient (m)

Cp specific heat capacity (J/ (kg.K)),

CV Controlled variable

D diameter (m)

Davg average forward step (m)

��

particle diameter(m)

Dout outside diameter(m)

EAa error in slope after break point (Equation E7)

EAb error in slope before point (Equation E7)

Eca error in intercept of the line before break point (Equation E6)

Ecb error in intercept of the line after break point (Equation E6)

ii

E(t) exit-age distribution function (minutes-1)

�� particle restitution coefficient

F mass flow rate (kgwet solid/s)

ffc flow index

Fr Froude number

��

acceleration of gravity (m/s2)

�� radial distribution function

Gu Gukhman number

h height of curtain (m)

hc convective heat transfer (J/( m2.s.K))

hm mass transfer coefficient (kg/(m2.s.Pa))

H holdup (kgwet solid)

�� enthalpy energy (J/kg)

� , latent heat of vaporization (KJ/kg)

ℎ"# internal convective heat transfer coefficient

ℎ$%& external convective heat transfer coefficient

ℎ'()*+ internal radiation heat transfer coefficient

ℎ'(),-. external radiation heat transfer coefficient

/0 heat transfer factor

/1 mass transfer factor

k2, k3, k4 transport coefficients (s-1)

k turbulence kinetic energy (m2/s2)

kg thermal conductivity of gas (W/m oC)

iii

23,-. thermal conductivity of gas based on shell temperature(W/m oC)

Kh correction factor for convective heat transfer coefficient

Kp steady state process gain

4 � unit stress tensor

L length of the dryer (m)

Ls length of flighted section (m)

M molar flow rate (kmol/hr)

5 mass (kg)

ms mass per length (kg/m)

maft mass averaged fall time (s)

mafh mass averaged fall height (m)

5�)6�"3# Passive mass at design loading condition (kg)

7)6�"3#898 total holdup (kg)

MW Molecular weight (kg/kmol)

n number of moles (mol)

?c number of cells (-)

:; number of flight (-)

P pressure (kg/m s2)

Pr Prandtl number

<=>>>> pressure and volume in ideal gas equation

Q heat (J/s)

"# inside radius(m)

iv

R ideal gas constant (J/(mol·K))

Ra Rayleigh number

Rj resistance

Ro outside radius (m)

Re Reynolds number

RF flight tip radius (m)

Rw drying rate (kg/s)

S cross sectional area of dryer (m2) (Equation 6.40)

Sc Schmidt number

Sh Sherwood number

St Stanton number

s1 flight base length(m)

s2 flight tip length (m)

SEG standard error of G in equation D4

SEH standard error of H in equation D4

SF scale accumulation factor

T temperature (oC)

t time (s)

?�( active cycle time (s)

?�� passive cycle time (s)

U velocity vector (m/s)

@

velocity fluctuations (m/s)

us solid velocity (m/s)

v

A� Internal energy (J/kg)

@B� , @>C

mean velocity components (m/s)

vg gas velocity (m/s)

X holdup, % of dryer volume (%) (Equation 6.40)

�D9E mole fraction of carbon dioxide in hot gas (kmol/kmol)

XDO mole fraction of oxygen in air (kmol/kmol)

XD? mole fraction of nitrogen in air (kmol/kmol)

Xcw mole fraction of water in air (kmol/kmol)

XFC mole fraction of carbon in fuel oil(kmol/kmol)

XFH mole fraction of hydrogen in fuel oil(kmol/kmol)

XFs mole fraction of sulphur in fuel oil(kmol/kmol)

XFw moisture content in fuel oil (kg/kg)

�0E9 moisture content in hot gas (kg/kg)

X? mole fraction of nitrogen in hot gas (kmol/kmol)

�F9E mole fraction of sulphur dioxide in hot gas (kmol/kmol)

xi , xj

direction coordinates (in Equations 4.14 and 4.15)

xw

moisture content (kg/kgwet solid)

xt tracer concentration (kg/kg)

yw gas humidity (kg/kg)

ijY

kth measured value of variable j in experiment i (Equation 5.22)

Yij jth predicted value of variable j in experiment i (Equation 5.22)

GI

gas humidity (mol/mol)

vi

z direction coordinate

∆K length (m)

Greek letters

℘ axial dispersion coefficient (m2/s)

℘AB mass diffusivity (m2.s−1)

α1 flight base angle (o)

α2 flight tip angle (o)

L

volume fraction (-)

M interphase transfer coefficient (kg/m3 s)

ϑ, α and βi, set of model parameters to be estimated (Equation 5.22)

N

voidage (-)

εr emissivity

ε dissipation rate of turbulent kinetic energy(m2/s3)

τ mean residence time (Equations 2.1 and 3.5) (minutes)

τ stress tensor (Equations 4.3 and 4.4)

θ slope of the drum (radians)

θAL area correction factor for the unflighted sections

θa area correction factor for the flighted sections

OP mass averaged discharge location (degrees)

θk kilning angle (radians)

OQ$�� heat loss turning factor

O� granular temperature ( m2/s2)

vii

R� bulk viscosity (kg/m s)

µ dynamic viscosity (kg/m s)

S� shear viscosity (kg/m s)

µt turbulence viscosity (kg/m s)

T

density (kg/m3)

U"C� variance of the jth measurement of variable j in experiment i (Equation 5.22)

U� second moment of RTD (minutes-2)

UV, U� effective turbulent Prandtl numbers for the transport of ε and k.

U' Stefan-Boltzmann constant

W dynamic angle of repose (o)

ℛ mass ratio of airbone to flight-borne solids

Y drum rotational speed (rad/s)

Ψ mass averaged properties

Subscripts

a active phase

AL active layer

amb ambient

b bulk

c combustion air

ct curtain

conv convection

D dilution air

viii

F Fuel oil

f first unloading flight

g gas phase

i, j directional coordinates

loss heat loss

p passive

pt particle

n last flight to discharge solid material

rad radiation

s solid

Tot total holdup in the dryer

v vapour

w water

1

ABSTRACT

Rotary dryers are commonly used in the food and mineral processing industries for drying

granular or particulate solids due to their simplicity, low cost and versatility compared to other

dryers. The co-current industrial rotary dryer (MMG, Karumba) examined in this study is used in

drying zinc and lead concentrate. The dryer is 22.2 metres long with a diameter of 3.9 metres.

The slope and the typical rotational speed of the dryer are 4 degrees and 3 rpm respectively. The

dryer has both unflighted and flighted sections with different flight configurations. Operational

issues associated with the dryer that lead to the requirement for a dynamic model of the dryer

include issues such as high fuel consumption and the build-up of scale on the internal surfaces.

In order to operate an optimum dryer, it is necessary to understand the mechanisms occurring

within the dryer. The important transport mechanisms that govern the performance of rotary

dryers are: solids transportation, heat, and mass transfer. Studies have shown that the knowledge

of the solid transport is important to solve the heat and mass transfer differential equations that

describe completely the temperature and moisture content profiles along the dryer for both solid

and gas phases. Solid transport within the dryer can be characterised through the solid residence

time distribution, which is the distribution of times taken for the solids to travel through the

dryer. Solid residence time distribution can be determined experimentally. The most common

experimental approach is to introduce tracer at the inlet and monitor tracer concentration at the

outlet as a function time. Several modelling approaches have been taken to determine the

residence time and the residence time distribution and these approaches have varied from

empirical correlations to compartment modelling. In many of these approaches, loading state,

residence time and operational feed rates are strongly linked. The loading state also influences

2

the effectiveness of particle to gas heat and mass transfer as well as the residence time

distribution of solids through the dryer.

There are three potential degrees of loading in a rotary dryer namely under-loaded, design loaded

and overloaded. However, most industrial rotary dryers are operated at under-loaded or

overloaded, which results into poor efficiency of the dryer and the optimal economics of the

dryer will not be achieved. As such, accurate estimation of the design load is critical to the

optimal performance of flighted rotary dryers and is an important characteristic of flighted rotary

dryer models.

To experimentally characterise MMG rotary dryer, industrial and laboratory experiments were

undertaken. The industrial experiments included residence time distributions (RTD), shell

temperature measurements, spatial sampling of the solids along the length of dryer, moisture

content analysis and Process Information (PI) data collection. Residence time distribution

experiments were carried out by injecting lithium chloride as tracer at the inlet of the dryer while

sampling outlet solids over a period of time. Zinc concentrate properties such as dynamic angle

of repose, bulk density and particle size were also determined. A series of different experiments

were undertaken to examine the effect of speed and loading.

Flight loading experiments were carried out at pilot scale to determine the effect of moisture

content and rotational speed on dryer design loadings and to facilitate accurate determination of

model parameters. The flight holdup experiments involved taking photographs of the cross-

sectional area of the dryer. An image analysis technique was developed to estimate the amount of

material within the flights and in the airborne phase. The analysis involved developing a

combined ImageJ thresholding process and in-house MATLAB code to estimate the cross-

3

sectional area of material within the flight. The suitability of the developed methodology was

established. In addition, saturation of both the airborne and upper drum flight-borne solids was

observed.

To select an appropriate geometrically derived design load model, comparison of existing design

load models from the literature was undertaken. The proportion of airborne to flight-borne solids

within the drum was characterised through a combination of photographic analysis coupled with

Computational Fluid Dynamics (CFD) simulation. In particular, solid volume fractions of the

airborne solids were characterised using a CFD technique based on the Eulerian-Eulerian

approach. The suitability of using geometric models of flight unloading to predict these

proportions in a design loaded dryer were discussed and a modified version of Baker’s (1988)

design load model was proposed.

A multiscale dynamic mass and energy process model was developed and validated for the dryer

in order to characterise the performance of MMG rotary dryer. The mass and energy balance

equations involved ordinary differential equations for describing the flighted sections and partial

differential equations for modelling the unflighted sections. Solids in unflighted sections were

modelled as the axially-dispersed plug flow system. In the flighted sections, the solids were

modelled using a compartment modelling approach involving well-mixed tanks (Sheehan et al.,

2005). The gas phase was modelled as a plug flow system. Simulations were undertaken using

gPROMS (process modelling software). As much as possible, model coefficients were

determined using geometric modelling based on material properties and dryer operational

conditions. The use of this approach is termed a pseudo-physical compartment model. The solid

transport model was validated using full scale residence time distribution at different

experimental conditions. The model results predicted well the effect of rotational speed, internal

4

diameter and solid feed rate. Estimated parameters included the kilning velocity, axial dispersed

coefficient and area correction factors. The validation of the energy balances was based on

Process Information (PI), experimental residence time distribution and moisture content data of

the studied dryer. Model parameters involving the surface area in contact with the incoming gas

data were manipulated to fit experimental moisture content. The gas and solid temperature

profiles were also predicted, which provide a firm basis upon which additional studies may be

undertaken.

Gas inlet temperature was identified as the most suitable manipulated variable for the dryer with

clean internal condition. However, to achieve desired product quality within a scaled dryer, the

study suggested the solid feed rate should be reduced so as to achieve optimum gas-solid

interaction. To address the high fuel consumption associated with the dryer, the study proposed

externally lagging of the dryer and reduction in the gas inlet temperature to meet the desired

product quality.

1

CHAPTER O E

1. I TRODUCTIO

Flighted rotary dryers are commonly used in the food and mineral processing industries for

drying granular or particulate solids. The rotary dryer consists of a cylindrical shell slightly

inclined towards the outlet as shown in Figure 1.1 and is fitted internally with an array of flights.

The arrangement and type of flights vary with the nature of the granular solids. As the dryer

rotates, solids are picked up by flights, lifted for a certain distance around the drum and fall

through the gas stream in a cascading curtain (see Figure 1.2). Gas used as drying medium is

introduced as either co-current or counter-current to the solid flow. The movement of solids

through the dryer is influenced by the following mechanisms: lifting by the flights, cascading

from the flights through the air stream and bouncing, rolling and sliding of the particles on

impact with the bottom of the dryer (Yliniemi, 1999).

Figure 1.1: Typical example of a co-current rotary dryer

Dried solid

Cool moist gas Hot gas

Wet feed

2

Figure 1.2: Cross-section of typical flighted rotary dryer showing the solids cascading

1.1 Motivation

The co-current industrial rotary dryer examined in this current study is used in drying zinc and

lead concentrates (MMG, Karumba, 2008–2010 seasons). The dryer has both unflighted and

flighted sections. Each flighted section has different flight configuration, although all flights are

standard two-stage designs. Operational issues associated with the dryer include high fuel

consumption and it is a challenge to operate the dryer effectively when there is hard scale build-

up on the internal surfaces.

Previous studies (Alvarez & Shene, 1994; Kelly, 1995; Cao & Langrish, 2000) have also

identified some other factors that affect the design and performance of a rotary dryer which

include the following: physical properties of the solids, geometrical configuration of the dryer

and flight geometry, gas-solid interactions and operating conditions such as solid feed rate, solid

inlet temperature, gas inlet flow rate, gas inlet temperature and rotational speed of the dryer.

3

For better understanding of the dryer’s performance, modelling can be undertaken at different

scales such as unit operation scale, flight scale, curtain and particle scale. The unit operation

scale models the overall process. Flight scale represents the flight loading capacity as it

facilitates the gas-solids interaction. The curtain and particle scale characterises the solid

properties such as dynamic angle of repose, bulk density and particle size.

The performance of rotary dryer is dictated by three important transport mechanisms, namely:

solids transportation, heat and mass transfer (Prutton et al., 1942; Matchett & Baker, 1987;

Renaud et al., 2000). However, studies have established that the solid distribution in the dryer

affects the movement of solids within the dryer, and as well as the amount of contact surface

between the gas and the solid (Duchesne et al., 1996; Sheehan et al., 2002). In rotary dryers,

there are three loading states: under-loaded, design loaded and overloaded. The loading capacity

of the dryer has been a key requirement to the prediction of the solid transport within the drum. It

is important to operate the dryer at design loading capacity to achieve optimum gas-solids

interaction. Design load models in literature have under-estimated or over-estimated the solid

distribution within the dryer (Lee, 2008), which greatly affects the quantity of solids undergoing

drying.

Solid transport in a rotary dryer is characterised through the interpretation of the solid residence

time distribution (RTD). This solid residence time is referred to as the time required for the solid

to travel the length of the dryer and it can be determined through experiment or modelling. The

experimental approach involves introducing a tracer at the inlet of the dryer and the tracer

concentration is monitored at the outlet as a function of time.

4

Modelling approaches of unflighted and flighted rotary dryers are different. To the best of the

author’s knowledge, there is no literature that combines the modelling of both unflighted and

flighted sections within a dryer. Previous studies have modelled the solid transport in an

unflighted rotary dryer using empirical correlations (Sullivan et al., 1927; Perron & Bui, 1990)

and plug flow models (Sai et al.; 1990; Ortiz et al., 2003; Ortiz et al., 2005). There have also

been substantial studies on the modelling of the flighted rotary dryer, which includes empirical

correlations, mechanistic models and compartment models. The empirical correlation and

mechanistic models do not account for the loading capacity and the effect of the flight

configuration and solid properties. The compartment modelling approaches were developed to

provide a more predictive means to estimate the residence time distribution. In recent examples

of compartment modelling by Sheehan et al. (2005) and Britton et al. (2006), they considered the

dryer geometry, solid flow properties and also the drag effect of the air stream on the solids. The

model parameters were estimated based on physical descriptions (described in Britton et al.

(2006)) and on geometric modelling of flight unloading (described in Britton et al. (2006) and

validated experimentally in Lee and Sheehan (2010)). The accurate estimation of the design load

and loading state of the dryer directly influenced determination of model parameters and the

mass distribution between the compartments representing the airborne and flight-borne solids.

Although there are several published works that deal with steady-state modelling of a rotary

dryer (Cao & Langrish, 2000; Shahhosseni et al., 2001; Iguaz et al., 2003; among others), there

are few examples of dynamic models of rotary dryers (Duchesne et al., 1997). Models are used

to predict the moisture content and temperature profiles of both phases (gas and solids) inside the

dryer. These models differ in describing the drying rate, the effect of operating conditions, the

solid residence time and the heat transfer. Drying occurs at different scales and it is important

5

that the different scale processes are taken into consideration. A multiscale model is necessary to

address the complex nature of gas-solids flow in the dryer.

1.2 Objectives and aim

The aim of this study is to develop a dynamic multiscale model, which will enable and improve

design and control of rotary dryers. Important information such as residence times, process input

and output parameters, and energy usage can be gained from industrial dryer experimentation.

However, laboratory-based and computer-based studies are required to understand and model the

internal particle and flight scale phenomena that occurs. The objectives of the study are as

follows:

• To develop a dynamic multiscale model to describe the MMG rotary dryer.

• To validate and optimise different scales model based on the results of industrial and

laboratory experimentation.

• To utilise the overall model to determine design and control strategies to optimise dryer

performance.

1.3 Structure of thesis

The thesis is divided into eight chapters:

• Chapter 1 provides the background, the aims and objective of the research.

• Chapter 2 presents the literature review on hold-up and residence time of the dryer.

Previous studies on modelling of unflighted and flighted rotary dryers are also discussed.

• Chapter 3 presents the methodologies and results of the industrial testing and

characterisation, which include residence time distribution trials, shell temperature

measurement, PI data collection and properties of zinc concentrates.

6

• Chapter 4 focuses on the estimation of design loading capacity in a flighted rotary dryer.

The chapter covers the flight loading experiments and detailed image analysis techniques

used to analyse the photographs taken during the experiments. The effect of rotational

speed and moisture content on design loading is also investigated. A combination of

image analysis calculations and Computational Fluid Dynamics (CFD) simulation to

estimate the masses of airborne and flight-borne solid is discussed. The content of this

chapter has been accepted for publication in the following journals:

o Ajayi, O.O., Sheehan, M.E., 2012. Design loading of free and cohesive solids in

flighted rotary dryer. Chemical Engineering Science Journal (in press).

o Ajayi, O.O., Sheehan, M.E., 2011. Application of image analysis to determine

design loading in flighted rotary, Powder Technology Journal (in press).

• Chapter 5 covers the development and validation of a solid transport model for the MMG

industrial rotary dryer. Parameter estimation techniques and results are discussed.

Verification of the model structure and parameters is also examined. The content of this

chapter was published in the following conference proceeding:

o Sheehan, M.E., Ajayi, O.O., Lee, A., 2008. Modelling solid transport of industrial

flighted rotary dryer. In, Proceedings of 18th European Symposium Computer

Aided Process Engineering (ESCAPE), 2008, June 1–4, Lyon, France.

• Chapter 6 presents the development and incorporation of the energy equations into the

validated solid transport compartment model. Parameter estimation technique and model

verification are discussed.

7

• Chapter 7 discusses the approach to identify manipulated variables for unscaled and

scaled conditions within the dryer. Engineering design options to reduce fuel

consumption were examined.

• Chapter 8 presents the conclusion of the research.

8

CHAPTER 2

2. LITERATURE REVIEW

The literature review covers previous studies on holdup and mean residence time of rotary

dryers. Various models used to estimate the design loading condition in rotary dryers will be

discussed. The review will also outline the modelling approaches of both flighted and unflighted

rotary dryers and highlight their deficiencies.

2.1 Holdup

There are two key property characteristics in dryer performance: residence time (RT) and hold-

up. The relationship between these key properties is expressed in Equation 2.1.

Z = � 2.1

where H, F and τ are the hold-up, feed rate and residence time respectively.

Holdup is defined as the amount of solids within the dryer. Holdup is further characterised into

airborne solids, and flight and drum borne solids, which are the solids within the flights and the

base of the drum. The degree of flight loading is affected by the operating conditions, physical

properties of the solid and the geometrical configuration of the dryer (Kelly, 1992). The

importance of flight loading cannot be underestimated because the proportion of airborne solids

to flight-borne solids dictates the extent of gas-solids interaction. The distribution of solids also

affects the residence time because of the difference in the rate of axial advance of airborne solids

and flight-borne solids. In many of the flighted rotary dryer (FRD) models in the literature, this

proportion has been approximated to between 10 and 15% of the total holdup and is typically

considered invariant to loading state.

9

2.1.1 Design load

In the rotary dryer, there are three potential degrees of loading namely under-loaded, design

loaded and overloaded. A dryer is defined as operating in an under-loaded condition when the

flights are not full to their capacity and unloading of the flight occurs after the 9 o'clock position

as shown in Figure 2.1a. A design loaded dryer is one in which the flights are at their maximum

capacity and the unloading of the flight occurs precisely at the 9 o'clock position as indicated in

Figure 2.1b. The design load condition is commonly assumed to represent the point of operation

where there is maximum interaction between the drying gas and the airborne solids. A dryer is

classified as overloaded when there are more solids present than required to fill the flights, as

illustrated in Figure 2.1c. In this situation, there is unloading of flights before the 9 o'clock

position and the excess solid rolls in the base of the dryer.

The fundamental assumption in flighted rotary drying is that the kilning or rolling solids do not

participate in drying to the extent that airborne solids do. As a result, their thermal and physical

interactions with the gas phase are often ignored in models. It can be reasonably assumed that the

operation of a dryer at under-loaded or overloaded conditions results into poor efficiency of the

dryer. Consequently, the design load of a dryer is an important parameter that should be

determined for optimisation, design and modelling of FRD.

Figure 2.1a: Under-loaded dryer

solids are discharged late in the rotation)

Figure 2.1b: Intermediate loading assumed close to design

discharge at precisely the 9 o'clock position

dryer (Arrow indicates the 9 o'clock position and demonstrates that

solids are discharged late in the rotation)

Intermediate loading assumed close to design load (Arrow

discharge at precisely the 9 o'clock position)

10

(Arrow indicates the 9 o'clock position and demonstrates that

(Arrow shows there is

11

Figure 2.1c: Overloaded dryer load (Arrow shows there is discharge before 9 o'clock position)

Previous studies have used geometric models of flight cross sections to estimate the design load

(Porter, 1963; Kelly & O’Donnell, 1977; Baker, 1988; Sherritt et al. 1993). Wang et al. (1995)

developed a geometric model to determine the amount of solids contained within the two-section

flight. Their geometric model was a function of flight angular position, drum rotational speed

and solid properties (dynamic angle and bulk density). Revol et al. (2001) also investigated the

effect of flight configuration on the volume of solids within the flights using image analysis. The

authors observed that the accurate estimation of the dynamic angle of repose was a function of

the flight geometry. Lee and Sheehan (2010) developed and validated a geometric unloading

model. The model described the amount of solid within the flight at different angular position.

Their model assumptions are: solids are free-flowing and there is a continuous unloading

process. However, photographic analysis showed that the unloading process was discontinuous

and the dynamic angle of repose was not constant throughout the unloading process due to an

avalanching discharge pattern of solids. Despite these experimental observations, the model

12

results and experimental data were comparable, which indicated the model assumptions were

appropriate for the unloading process.

The most commonly used design load model is Porter's assumption (Porter, 1963), described in

Equation 2.2 (Sheehan et al., 2005). Porter’s assumption is based on the concept that at full flight

at design loading, there are sufficient solids to fill half of the total flights. In this case, a full

flight is defined as the solids in the 9 o'clock flight. Kelly and O’Donnell’s (1977) model

presented in Equation 2.3 used a different type of flight to that of Porter (equal angular

distribution flight). In all of these models, the total holdup was determined, which includes flight

and airborne solids. Matchett and Sheikh (1990) invalidated Porter’s assumption based on the

photographic evidence that the holdup within a flight is a function of flight geometry. Their

photographic evidence showed that with different flight configurations, maximum flight loading

was not consistent. This indicates a lack of universality for Equation 2.2, despite its widespread

use.

78$& = 7\]\ × :;2 2.2

78$& = 7\]\ × `:; + 12 c 2.3

7\]\ is the mass at the 9 o'clock position, TotM is the total hold-up of the dryer at design point

including both airborne (active) solids and flight-borne (passive borne) solids and :; is the total

number of flights.

Baker (1988) proposed a model to determine only the flight-borne solids (Equation 2.4). The

model was based on the assumption that the holdups of flights in the lower half of the drum are

13

the same as the holdups of the flights in the upper half of the drum. Baker’s model involves

calculating the amount of the solids in each flight above and including the 9 o'clock flight.

7)6�"3# = d2 × e 7"#; f − 7\]\ 2.4

designM is the design load based on the passive phase (TP) only and excludes airborne solids.

iM is the mass in each flight (i) with subscripts f and n referring to the 9 o'clock flight and last

discharging flight respectively.

In an alternative study, Sherritt et al. (1993) developed a geometrically driven integral model of

flight discharge. Their model was capable of predicting drum and more specifically airborne

holdup, for under, design and overloaded dryers. Their model was predicated on knowing the

initial discharge location for the first unloading flight and assumed a mirror image, with respect

to loading, in the upper half and lower half flights, similar to Baker's (1988) model assumptions.

However, their model was not generic with respect to flight geometry and a comparative study

by Hatzilyberis and Androutsopoulos (1999) showed lower levels of predictive ability for

rotating drums fitted with equal angular distribution (EAD) flights.

2.2 Residence time

Solid transport within the dryer is typically characterised through determination of the solid

residence time which is the time required for an average solid particle to travel the length of the

dryer. However, when the particles move through the dryer during normal operation, they do not

all take the same path to exit. Dispersion is typical in an industrial flighted rotary dryer. In order

to characterise the solid transport and dispersion within the dryer, residence time distributions are

determined (Renaud et al., 2000; Sheehan et al., 2005). Studies have determined the solid

14

residence time using an experimental approach (Perron & Bui, 1990; Duchesne et al., 1996;

Renaud et al., 2000; Renaud et al., 2001; Sheehan et al., 2005).

Studies have examined various parameters that affect the mean residence time of a rotary dryer

(Renaud et al., 2001; Yang et al., 2003; Lisboa et al., 2007). Renaud et al. (2001) analysed the

effect of a solid’s feed moisture content on the mean residence time. Solid moisture content

significantly affected the mean residence time and the shape of the residence time distribution

(RTD). The high moisture content, the solids (in this case: sand used in cement make-up)

resulted in a longer mean residence time and also altered the shape of RTD.

Yang et al. (2003) developed a dynamic experiment based on a step change of feed throughput to

determine solid holdup and mean residence time in a pilot scale rotary dryer. It was observed that

the rotational speed had a significant effect on the discharge solids flow rate and the average

residence time. Furthermore, with increase in the feed rate throughput, there was an increase in

the mean residence time. The authors noticed a linear relationship between the slope of the dryer

and the mean residence time. Many of these observations confirm the general form of empirical

residence time equations such as Friedman and Marshall (1949a). The authors concluded that the

mean residence time is significantly affected by the changes in the flow properties of the solids

which depend on moisture content. The most important of these properties is the dynamic angle

of repose. This conclusion agrees with earlier findings of Renaud et al. (2001).

Matchett and Baker (1987) and Kelly (1992) concluded that flight design was a contributing

factor in the accurate estimation of the mean residence time. Lisboa et al. (2007) investigated the

performance of the dryer in relation to the number of flights and concluded that both residence

15

time and drying rate increased with number of flights. The study further established that

increasing rotational speed resulted in low residence time.

2.3 Modelling approaches

Proper modelling of solid transport is important because residence time distribution and holdup

significantly influence the drying process and prediction of many important process variables

such as outlet moisture content and temperature. Modelling approaches for flighted dryers and

unflighted dryers are different. In addition, to the best of the author’s knowledge, there is no

study in literature that combines the modelling of both unflighted and flighted sections within the

dryer.

Models of flighted rotary dryers in the literature include empirical correlations, semi-empirical

correlations, mechanistic, and compartment modelling. A comprehensive review of empirical

correlations, semi-empirical correlations and mechanistic models can be found in Lee (2008).

Empirical correlations and mechanistic models are simplified approaches and do not account for

the effect of flight configuration and solids properties. In light of these shortcomings, the

compartment modelling approach was developed. This approach utilises series-parallel

formulation of well-mixed tanks commonly used in reaction engineering (Levenspiel, 1999). A

recent example of a geometrically driven compartment modelling approach by Sheehan et al.

(2005) and Britton et al. (2006) tested the pseudo-physical compartment model and provided a

restructure for solid flow paths, which gave the actual representation of the dynamics in the

rotary dryer. The model considered the dryer geometry, flight configuration, solid flow

properties and also the drag effect of the air stream on the solids. It can be concluded that an

appropriate solid transport model for a rotary dryer should have the following characteristics:

16

ability to consider the effect of flight configuration, proper distribution of solid in the dryer, solid

properties should not be ignored, and ability to account for different loading state.

2.3.1 Unflighted dryer

Previous studies in unflighted dryer modelling have assumed that solids move in plug flow with

(Danckwerts, 1953; Fan & Ahn, 1961, Mu & Perlmutter, 1980; Sai et al., 1990) or without (Ortiz

et al., 2003; Ortiz et al., 2005) axial mixing. However, experimental RTD studies have shown

that axial dispersion occurs both in unflighted and flighted dryers (Sai et al., 1990; Sheehan,

1993). In some unflighted dryer studies, empirical correlations were developed from RTD

experiments (Sullivan et al., 1927; Perron & Bui, 1990). Fan and Ahn (1961) used the classic

diffusion model stated in Equation 2.5 (Levenspiel, 1999) to simulate the dispersion and

residence time distribution of solids in a rotating cylinder. It should be noted that Equation 2.5

only holds for no net solid flow system

h��h? = ℘ h��hK� 2.5

where C, t, ℘ and z are concentration, time, dispersion coefficient and length respectively.

Sai et al. (1990) also proposed the use of an axial dispersion model with an appropriate Peclet

(Pe) number estimated via experiments. In their study, the effects of operating conditions such as

solid feed rate, rotational speed and dam height on the mean residence time were investigated. In

another study, Kohav et al. (1995) used stochastic algorithms to determine the effect of

segregated rolling or slumping distance on the axial dispersion in rolling and slumping beds.

17

2.3.2 Flighted rotary dryers

Matchett and Baker’s (1987) mechanistic model was the definition work for differentiating the

solids within the drum into two phases, namely: the airborne solids and flight and drum-borne

solids. The airborne solids contain the particles falling from the flight acted upon by both gravity

and drag due to airflow, i.e. the cascading flow. The flight and drum-borne solids are solids that

remain in the flights and the drum base.

Compartment modelling approaches were developed as they provide a convenient structure to

match the typical residence time distribution curves found in flighted rotary dryers. Duchesne et

al. (1996) proposed a modified Cholette-Cloutier (1959) model, which accounts for the presence

of dead zones. Sheehan et al. (2005) developed a pseudo-physical compartment model. Their

model treated the solids as active and passive phases. The active phase consists of solid particles

in contact with incoming drying gas while the passive phase does not participate in the drying

process (Figure 2.2). Figure 2.3 shows their model structure, which describes the flow path into

the active and passive phase.

Figure 2.2: Active and passive phase (Sheehan et al., 2005)

18

Figure 2.3: Model structure

There have been substantial rotary dryer models in the literature which have been used to predict

the moisture content and temperature profile inside a dryer (Douglas et al., 1993; Cao &

Langrish, 2000; Shahhosseni et al., 2001; Iguaz et al., 2003). These models differ in the way the

drying rate, heat transfer and the residence time are described.

Douglas et al. (1993) developed a model based on heat and mass balance to illustrate the effect

of changes in inlet conditions on the outlet conditions of sugar dryers. Both the residence time

and volumetric heat coefficient were calculated using Friedman and Marshall (1949a) and

Friedman and Marshall (1949b) empirical correlations respectively. The effects of flight

geometry and solid distribution were not considered.

Wang et al. (1993) developed a generalised distributed parameter model for a sugar dryer. The

heat transfer coefficients were calculated using three different correlations for comparison. These

correlations include Freidman-Marshall (1949), Ranz-Marshall (1952), and Hironsue (1989). The

gas phase was modelled as a plug flow system and the residence time was calculated via the

Friedman and Marshall (1949) model. The authors concluded that a dynamic rotary dryer model

should be developed to account for effect of the flight geometry and of solid distribution within

the dryer.

i i-1 i+1 Active phase

Passive phase

19

Duchesne et al. (1997) developed a dynamic simulator of a mineral concentrate rotary dryer,

which consisted of a furnace model, a solid transport model and a gas model. Their modelling

approach was different from previous studies (Douglas et al., 1993; Wang et al., 1993; Perez-

Correa et al., 1998) in that solid transport was modelled using the compartment model approach.

The predicted and measured values of the outlet variables such as moisture and gas temperature

were comparable.

Cao and Langrish (2000) also developed an overall system model for a counter-current,

cascading dryer. The model used heat and mass balances around the dryer, together with the

Matchett and Baker (1988) mechanistic residence time model. The heat-transfer correlation of

Ranz and Marshall (1952) was used. Limitations to the Matchett and Baker (1987) mechanistic

model included the requirement for an empirical holdup number determined through dryer

specific experiments.

To further achieve a suitable model for rotary dryer, Shahhosseni et al. (2001) proposed an

adaptive modelling strategy that combines on-line model identification with well-known

conservation laws. The drying rates, the heat and mass transfer coefficients were empirically

fitted based on online measured data instead of the conventional approach of using empirical

correlations. The solid residence time was calculated using the modified Friedman and Marshall

(1949a) correlation previously developed by the authors (Shahhosseni et al., 2000).

Didriksen (2002) presented a dynamic model for a rotary dryer, which comprises of heat and

mass balances together with Kelly and O’Donnell (1968) total hold up time empirical

correlation. The model showed good predictive capabilities and was used in model-based

predictive controller (MPC) configuration. In another study, a model for the dehydration of

20

vegetable by-products in a rotary dryer was proposed (Iguaz et al., 2003). The model

incorporated heat and mass balances around the dryer, the residence time model of Friedman and

Marshall (1949), and the heat transfer correlation of Myklestad (1963).

Ortiz et al. (2005) proposed a dynamic simulation system for a pilot scale rotary kiln used in

manufacturing activated carbon. Perry and Green’s (1984) empirical model was used to predict

the residence time. Their study assumed there was neither solid nor gas axial mixing and both

phases were modelled as plug flow systems. Raffak et al. (2008) presented also a dynamic model

for a phosphate rotary dryer. The model was based on the equations of heat and mass transfer

between the gas and solids phases. The mean residence time was estimated using Alvarez and

Shene’s (1994) empirical model. The predicted moisture and temperature for both phases well-

matched the experimental data.

Despite numerous models in literature, there remain deficiencies in the modelling of the solid

transport, which give rise to doubt regarding their abilities to accurately predict the moisture and

temperature profiles for both phases. Predominant deficiencies include that the loading state not

taking into consideration and the mean residence times were often estimated using empirical

correlations, which are invariant to solids moisture content and flight geometry, which are

known to have a significant effect on the mean residence time (Renaud et al., 2000; Renaud et

al., 2001; Yang et al., 2003) and residence time distribution. Thus, it is important to develop a

dynamic model that will address all of these limitations.

2.4 Summary

The literature review highlighted the need to develop a dynamic model for a rotary dryer because

most of the published works deal with steady-state modelling of a rotary dryer. In most of these

21

models, the modelling of the solid transport was based on either empirical correlations or

mechanistic models. These modelling approaches do not account for the effect of loading state,

flight geometry and solid properties.

To address these shortcomings, the compartment modelling approach was developed. The

approach consists of series-parallel formulation of well-mixed tanks whereby the compartment

numbers and model transport coefficients were derived through geometric modelling, based on

dryer geometry and solids physical properties. The compartment modelling approach will be

chosen for this work. In the compartment modelling approach, the loading state, residence time

and solid feed rate are strongly linked. The accurate estimation of the design load and loading

state of the dryer is an important characteristic of compartment modelling approach. Most design

load models have not been validated experimentally.

The studied dryer has both unflighted and flighted sections. Studies have shown that the

modelling approaches of the solid transport within unflighted and flighted rotary dryers are

different. Therefore, the axially-dispersed plug model characterised by a kilning velocity and

dispersion coefficient will be used in this study.

22

CHAPTER THREE

3. I DUSTRIAL SCALE TESTI G

This chapter describes the laboratory and industrial experiments that provide experimental data

for model validation. The geometrical configuration of the MMG co-current industrial rotary

dryer was verified and used as input data for the geometric modelling. The characterisation of

zinc concentrate properties (dynamic angle of repose, bulk density and particle size) was

discussed. The fitted equation for moisture content profile was used in initial solid transport

model fitting (Chapter 6) to account for axial variation in the dynamic angle of repose. The

experimental moisture content profile was used to validate the mass and energy balances

presented in Chapter 7. Heat transfer coefficient and contact surface area calculations in Chapter

7 were dependent on the assumed particle size profile.

The chapter also outlines the industrial experiments which include residence time distributions

(RTD), shell temperature measurement, spatial sampling of the solid along the length of dryer,

moisture content analysis and Process Information (PI) data collection. Internal temperature

profiles across the dryer were not determined because of the hazards involved in carrying out the

experiments within an industrial setting. The fuel and air properties were characterised through

the system description. The RTD curves generated in this chapter were used in the validation of

the solid transport model (Chapter 6) and in the mass and energy balance analysis (Chapter 7).

The shell temperature measurement was used to estimate the heat loss profile of the dryer

presented in Chapter 7. The error in PI output data was not determined.

23

3.1 Process description

Figure 3.1 shows the schematic diagram of the drying process. The drying process consists of the

combustion chamber and the rotary dryer. The industrial rotary dryer is used to dry zinc and lead

concentrate. The concentrate is fed into the dryer via a screw feeder. The typical solid inlet

moisture content varies between 16% and 18% and the outlet moisture content ranges between

12% and 12.5%. The hot gas enters the dryer at 500 oC via the combustion chamber. A

distributed control system (DCS) based on feed forward control is used to control the dryer. The

control algorithm of the DCS calculates the amount of water to be removed using the inlet and

outlet target moisture content, solid flow rate, air flow into the combustion chamber through the

fan opening, and determines the quantity of fuel oil required in the combustion chamber.

The Process Information (PI) is collected using sensors and this information is referred to as PI

data. Table 3.1 presents the operating variables measured via sensors and stored as PI data. The

shell temperature measurements were manually collected during RTD experiments. The

experiments were carried out at as steady state as possible. The averaged PI data and statistical

deviations for different experiments are outlined in subsequent sections.

24

Figure 3.1: Schematic representation of the MMG combustion chamber and industrial

rotary dryer

Table 3.1: List of measurements obtained via sensors

Process variable Units

Gas inlet temperature oC

Gas outlet temperature oC

Solid feed rate Tonnes/hour

Solid outlet temperature oC

Dilution air fan opening %

Combustion air fan opening %

3.2 Geometrical Configuration of the industrial dryer

The geometrical configuration of the dryer was verified during the scheduled shutdown for

maintenance and internal cleaning of the dryer. The dryer is divided into five sections (Figure

Wet feed

Dried solid

Cool moist gas Rotary dryer

Combustion

chamber

Dilution air

Combustion air

Fuel oil

Hopper

Screw feeder

25

3.2). Sections A and E are unflighted. Section A is fitted with chains to reduce the size of the

clumped solid entering the dryer. The granulation of the zinc concentrate into spherical particles

of 6–7 millimetres in size occurs at Section E. Sections B, C and D are fitted with internal flights

with different configurations in each section. Flight geometry measurements are presented in

Table 3.2. The dryer is 22.2 metres long with an internal diameter of 3.9 metres and inclined

towards the inlet at 4 degrees. Typical rotational speed is 3 rpm.

Figure 3.2: Geometrical details of the dryer (All length dimensions are in metres)

Table 3.2: Geometrical configuration of the drum

Section Length of

section (m)

Flight

base (m)

Flight tip

(m)

Flight tip angle

(o)

Flight base

angle (o)

umber

of flights

A 2.1 - - - -

B 2.4 0.120 0.210 135 90 30

C 3.3 0.130 0.220 150 90 30

D 6.6 0.120 0.210 130 90 30

E 7.5 - - -

Outlet Inlet E

2.1 2.4 3.3 6.6 7.5

D C B A

26

3.3 Characterisation of the combustion chamber

The gas flow rate into the MMG industrial rotary dryer is not directly measured. It is important

to characterise the combustion chamber so as to determine its outlet gas flow rate. Air enters the

combustion chamber and is heated by burning the fuel oil. The hot gas leaves the combustion

chamber at an approximate temperature of 500 oC. The block flow diagram of the combustion

chamber and its variables is outlined in Appendix A.

3.4 Physical properties of zinc concentrates

The study assumed the properties of zinc concentrate determined at a particular internal

condition of the dryer remain constant for all test runs. Samples of zinc concentrate were taken

along the length of the dryer prior to a shutdown and internal cleaning of the dryer. The dryer

was full of hot zinc concentrate during this spatial sampling. Samples were taken every one

metre (23 samples in total).

3.4.1 Moisture content profile

The moisture content for each sample was determined using the on-site MMG oven. A known

mass of zinc sample was placed in the preheated oven at 105 oC temperature. The sample was

measured after three hours and reheated for another one hour to ensure there was no moisture

content within the sample. The evaporated moisture content was calculated. Figure 3.3 shows the

moisture content profile along the length of the dryer. The data in Figure 3.3 was fitted using a

rational polynomial function to derive Equation 3.1, relating the moisture content to the dryer

length.

27

Figure 3.3: Moisture content profile along the length of the dryer

jI = 0.1006m + 2.218m + 13.51 3.1

where xw and L are the solid moisture content (kg/kgwet solid) and axial position within the dryer

(m) respectively.

3.4.2 Dynamic angle of repose

The dynamic angle of repose describes the flowability of solid within the flights. Experiments

were carried out in a pilot scale dryer by placing a subset of sampled zinc concentrate solid in a

container. The filled container was affixed to the front-end Perspex of the drum (see Figure 3.4).

Photographs of the front end of the rotating drum were taken and the dynamic angle of repose

was measured using ImageJ software.

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0 5 10 15 20

Mo

istu

re c

on

ten

t (k

g/k

gw

et s

oli

d)

Length along the drum (m)

Experimental data

Fitted data

28

Figure 3.4: Experimental apparatus to measure dynamic angle of repose

The dynamic angle of repose as a function of the corresponding moisture content of the solid is

shown in Table 3.3 and plotted in Figure 3.5. The fitted linear equation was used in all further

modelling to relate moisture content to dynamic angle of repose (Equation 3.2). The standard

deviation of the angle of repose reduces as the moisture content of the solid reduces. This is a

common observation with a decrease in solid cohesion (Lee & Sheehan, 2010).

φ

29

Table 3.3: Dynamic angle of repose

Position along the

length of the drum(m)

Moisture

content

Dynamic angle

of repose(o)

Standard

deviation(o)

0 0.166 60.6 4.7

3 0.150 56.6 4.4

6 0.142 54.2 4.3

9 0.138 48.8 4.0

14 0.132 46.8 2.6

15 0.128 45.6 3.3

21 0.124 43.4 2.4

23 0.120 43.3 0.9

Figure 3.5: Dynamic angle of repose versus moisture content

y = 419.65xw - 7.8018

R² = 0.9558

0

10

20

30

40

50

60

70

0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18

Dy

na

mic

an

gle

of

rep

ose

(o)

Moisture content (kg/kgwet solid)

30

∅ = 419.6jI − 7.801 3.2

where φ and xw are dynamic angle of repose (degrees) and the corresponding solid moisture

content (kg/kgwet solid) respectively.

3.4.3 Particle size

The particle size distribution of the zinc concentrate at different sections of the dryer was carried

out using dry sieving. Sieves used were 38 mm, 19 mm, 9.5 mm, 4.75 mm, 2.36 mm, 1.18 mm,

and 600 µm. The mass of solid in each sieve was measured. Thirteen samples of zinc concentrate

at different sections of the dryer were sieved. Samples n = 0 to 23 are zinc concentrates samples

taken at every one meter of the dryer. The mass percentage passing is plotted in Figure 3.6.

Figure 3.6: Mass percentage of the passing (Samples n = 0 to 23 are zinc concentrates

samples that were taken every one meter along the length of the dryer)

0

10

20

30

40

50

60

70

80

90

100

0.1 1 10 100

Cu

mm

ula

tiv

e p

erce

nta

ge

of

pass

ing

(%

)

Size (mm)

Sample 0

Sample 2

Sample 4

Sample 6

Sample 8

Sample 10

Sample 12

Sample 14

Sample 16

Sample 18

Sample 20

Sample 22

Sample 23

31

3.4.4 Bulk density

The consolidated bulk densities of the inlet and outlet solids were determined in the laboratory

(Table 3.4). The process involved weighing an empty 200 ml volumetric cylinder and filling it

with zinc concentrate. The cylinder was tapped until no more consolidation occurred and the

sample was measured. The consolidated bulk density was calculated using Equation 3.3. Density

measurements were repeated five times to determine averages and standard deviations.

Consolidated bulk density was assumed to change linearly with respect to moisture content

(Equation 3.4).

Tu = 7vww=xy@5� 3.3

Table 3.4: Consolidated bulk densities of the solid

Solid

Consolidated bulk

density (kg/m3)

Standard deviation

(kg/m3)

Inlet 1530 12

Outlet 1660 31

Tu = 2043.8 − 3095.2jI 3.4

where ρb and xw are bulk density (kg/m3) and moisture content (kg/kgwet solid) respectively.

32

3.5 Residence Time Distribution (RTD) Tests

3.5.1 Experimental studies

The residence time distributions (RTD) are usually obtained by tracer tests. In a tracer test, an

inert chemical (tracer) is injected at the inlet of the dryer while the concentration of the tracer at

the outlet as a function of time is monitored. There are two common ways to inject the tracer,

namely: pulse input and step change. The pulse input involves rapid injection of a known amount

of tracer and the outlet concentration is measured as a function of time.

The accurate determination of RTD largely depends on proper selection and introduction of the

tracer. Sheehan et al. (2002) presented residence time distributions for an industrial sugar dryer.

Three different tracer compounds were used in their experiment and a pulse tracer testing lithium

chloride solution produced the best results. Other studies have also used lithium chloride (LiCl)

as a tracer in both pilot scale and industrial rotary dryers (Renaud et al, 2000; Britton et al., 2006;

Owens, 2006). Important characteristics of a tracer are: analysis of the tracer should be

convenient, sensitive and reproducible, inexpensive, easy to handle and unable to be absorbed on

or react with the surface of the dryer.

The first moment of the RTD (mean residence time) and residence time distribution function

were calculated using Equations 3.5 and 3.6. As shown in Equations 3.5 and 3.6, the time limit

tends to infinity but the RTD experiments were truncated at finite time of 1.5 hours. After this

length of time, the Lithium concentrations were below background and because of their low

values were prone to high relative error. Curl and McMillan (1966) developed error models to

quantify the errors when estimating RTD moments at finite time. Their study found there was

significant error between the values estimated at infinity time and finite time. However, the

primary focus of this study was not specifically to determine mean residence time and other

33

moments of the distributions. The objective of the RTD study is to provide sufficient data for

fitting and validating the developed model in Chapters 5 and 6, in which case the error in

neglecting the tail was considered not significant.

Z = z ?{�?��?|� 3.5

where

{�?� = ��?�} ��?��?|$ 3.6

3.5.2 RTD test methodology

Previous characterization of MMG rotary dryer showed there was poor tracer recovery when

standard solution of lithium chloride was injected into the inlet of the dryer (Owen, 2006). As a

result, two different approaches to introducing the tracer into the inlet of the dryer were

investigated: preparation of a standard solution of lithium chloride (LiCl), and pre-mixing the

LiCl powder with a certain amount of zinc concentrate.

The lithium concentrations in the samples taken at the outlet were determined using Inductively

Coupled Plasma Mass Spectrometry (ICP-MS) available at the JCU Advanced Analytical Centre

(AAC). The background lithium concentration in the sample was determined to ensure its

concentration was low and would not interfere with the tracer analysis.

Each RTD test was carried out when the dryer was as close as possible to steady state. It was

difficult to have a complete steady state in an industrial setting considering all factors that affect

the steady operation of the plant. For example, the dryer feed rate is affected by the discharge

from the five batch filter presses used in the operation. Standard deviations from PI data were

used to quantify the variation. The Process Information (PI) data for the two approaches are

34

presented in Tables 3.5 and 3.6. The experimental procedures for the two approaches are

described below.

3.5.2.1 Tracer standard solution approach (Test 1)

1.25 kg of LiCl powder (99.0% purity, Chem-supply) was dissolved in four litres volume of de-

ionised water (51.15g lithium /L). The prepared tracer solution was injected into the dryer

directly, over a period of one minute. Solids are fed directly from the hopper to the dryer via a

screw feeder. The time taken for the solid to reach the inlet of the dryer from the hopper was

approximately 20 seconds. Samples from the outlet were taken at intervals of 30 seconds for the

first 30 minutes and every 60 seconds for the remaining 1.5 hours.

3.5.2.2 Solid tracer pre-mixed with inlet solid (Test 2)

1.25 kg of LiCl powder (99.0% purity, Chem-supply) was mixed thoroughly with 8 kg of inlet

feed and the prepared material was placed onto the inlet conveyor at the mouth of the hopper.

Samples from the outlet were taken at intervals of 30 seconds for the first 30 minutes and every

60 seconds for the remaining 1.5 hours.

35

Table 3.5: Operating conditions for Test 1

PI Description Average value Standard deviation

Solid feed rate 134 ton/hr 18 ton/hr

Gas inlet temperature 517 oC 41 oC

Solid inlet moisture content 17.6% 0.79%

Gas outlet temperature 155 oC 23 oC

Product outlet temperature 49 oC 2 oC

Product moisture content 11.9%

Rotational speed of the drum 3 rpm -

Internal condition Unscaled


PI Description Average value Standard deviation





Product outlet temperature 50 oC 1 oC

Product moisture content 12.5%


Internal condition Unscaled

36

3.5.3 Data analysis

To quantify the reliability of Residence Time Distribution (RTD) tests, the quantity of tracer

recovered from the outlet was determined by mass balance on lithium across the dryer and

compared to the quantity of tracer added to the dryer (Equation 3.7). Trapezoidal rule was used

to solve Equation 3.7 and that resulted in Equation 3.8.

~x?vy 5vww x� ?v�� = z �. �x@?�. �?&�

� 3.7

where C, F and tf are tracer concentration (kg/kg), solid flow rate (kgwet solid/s) and final trial time

(seconds) respectively

z �. �� v?��x@?�. �?&�

�= ∆? `��2 + �� + �� + ⋯ + �&&2 c 3.8

Raw data of lithium concentration versus time for the experiments can be found in Appendix B.

The solid tracer approach (Test 2) showed improved tracer recovery compared to the standard

solution approach (Test 1) and was used for all further RTD trials (Table 3.7). It can be

concluded that the tracer solution approach (Test 1) may lead to poor localized mixing and a

pulse of sludgy solids, which then increased the probability of zinc concentrates sticking to the

walls of the hopper or inlet of the dryer. Premixed concentrate provides more uniform mixing

and reduces the loss of tracer compound.

An assumption made in the treatment of the error in the RTD experimental data, was that the

variance in lithium concentration throughout the test remained constant. Comparing two data sets

for test 2 led to a standard error estimate of 0.15 ppm for each sample across the entire data set,

which was within the instrument error (range from 0.01 to 0.5ppm). It is assumed this is the case

37

for all tests undertaken. The standard error was within the bounds used in later model parameter

estimations to fit the model to the RTD data (range of 0.01 to 10ppm).

Figure 3.7: Lithium concentration versus time (for method testing RTD trials)

Table 3.7: Mass of lithium recovered

Approach Mass of lithium injected

to the dryer (g)

Mass of lithium

recovered (g)

Percentage of

recovery (%)

Test 1 205.9 127 60

Test 2 205.9 191 91

0

5

10

15

20

25

30

35

5 7 9 11 13 15 17 19

Tra

cer

con

cen

trati

on

(k

g/k

g)

Time (minutes)

Test 1 Test 2

38

3.5.4 RTD operational conditions

Using the premixed methodology for tracer injection, a series of RTD experiments were carried

out under different operating conditions. To determine the effect of scaling of flights and walls,

two tests were conducted: prior to a scheduled shutdown (Test 3) and just after a scheduled

shutdown where internal cleaning had occurred (Test 4). To determine the effect of rotational

speed, two tests were undertaken (Test 5: 2 rpm and Test 6: 3 rpm). The operating conditions and

tracer quantities for all RTD trials are presented in Tables 3.8–3.11.


Description Average value Standard deviation




Gas outlet temperature 165 oC 1.8 oC

Product outlet temperature 46 oC 0.3 oC

Product outlet moisture content 13.6% -


Internal condition of the dryer Scaled

Tracer quantity (LiCl powder) 2 kg

39




Gas inlet temperature 500 oC 16.05 oC






Internal condition of the dryer Unscaled







Gas outlet temperature 155 oC 7.98 oC


Product outlet moisture content 12% -




40












The results of the RTD tests are plotted in Figure 3.8. The percentages of tracer recovered during

the experiments are presented in Table 3.12. Test 3 had low recovery, which may be due to high

solid feed rate and the scaled internal condition of the dryer. The scale build-up in the dryer may

enhance the adhesion of the material resulting in loss of the tracer within the dryer. The

percentage recovery in Test 5 was also relatively low compared to other tests (Tests 2, 4 and 6)

with similar internal conditions.

41

Figure 3.8: Lithium concentration versus time for test runs

Table 3.12: Mass of lithium recovered

Condition of the dryer Actual Tracer (g)

(Li)

Recovered Tracer (g)

(Li)

Recovery (%)

Test 3 327.4 194 59

Test 4 327.4 307 94

Test 5 327.4 252 77

Test 6 327.4 273 84

The distribution of residence times is represented by an exit age distribution (E(t)). Equation 3.8

was used to transform the lithium concentration curves (Figures 3.7 and 3.8) into residence time

distribution curves (Figure 3.9).

0

10

20

30

40

50

60

5 10 15 20 25 30 35

Tra

cer

con

cen

trati

on

(k

g/k

g)

Time (minutes)

Test 3 Test 4

Test 5 Test 6

42

Figure 3.9: ormalised residence time distribution functions for all tests

Table 3.13 presents the first moment of the RTD trials. The most obvious observation is the

effect of rotational speed on mean residence time.

Table 3.13: Moment of RTD

Test

Condition of

Dryer

Rotational

speed (rpm)

Solid feed rate

(kgwet solid/min)

1st moment

τ (minutes)

Test 1 Unscaled 3 2230 13.20


Test 3 Scaled 3 3140 14.00




0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

5 10 15 20 25 30 35

o

rma

lise

d t

race

r co

nce

ntr

ati

on

(E(t

))

Time (minutes)

Test 1 Test 2 Test 3 Test 4 Test 5 Test 6

43

3.5.4.1 Hold-up

The hold-up of the dryer for the different operating conditions was calculated using Equation 2.1.

The average P1 data was used as the solid feed rate for all the conditions. The hold-up values for

all of the RTD trials are presented in Table 3.14.

Table 3.14: Holdup values for different conditions

Test

Condition of

Dryer

Rotational

speed (rpm)

τ

(minutes)

Solid feed rate

(kgwet solid/min)

Holdup

(kgwet solid)

Test 1 Unscaled 3 13.20 2230 29,400

Test 2 Unscaled 3 12.02 2840 34,100

Test 3 Scaled 3 14.00 3140 43,900

Test 4 Unscaled 3 15.21 2440 37,100

Test 5 Unscaled 2 21.73 1940 42,200

Test 6 Unscaled 3 15.61 2690 41,990

3.6 Shell temperature measurement

The shell temperature distribution across the length of the dryer was measured using an infrared

heat gun (Kane-May Infratrace 801). The measurement was undertaken both prior to and after

cleaning of the internal walls of the dryer. The gas inlet temperatures for the scale accumulated

dryer and the clean dryer were 501 oC and 498 oC respectively. Figure 3.10 shows the smoothed

shell temperature profiles of the scale accumulated and the unscaled dryer.

44

Figure 3.10: Shell temperature profile along the length of the dryer

40

60

80

100

120

140

160

0 5 10 15 20 25

Tem

per

atu

re (

oC

)

Axial position (m)

Scale accumulated dryer

Unscaled dryer

45

CHAPTER FOUR

4. DESIG LOADI G I FLIGHTED ROTARY DRYERS

The amount of solids contained within the flights and in the airborne phase of a flighted rotary

dryer is critical to the analysis of performance and the optimal design of these units. In order to

validate design loading states in flighted rotary dryers, there is a need to carry out experiments at

different solid loadings. Previous studies have described the determination of flight holdup using

photographs of the cross-sectional area of a rotating drum (Matchett & Sheikh, 1990; Revol et

al., 2001). This technique has also been used to determine angle of repose as a function of the

angular position of the flights and has demonstrated that accurate analysis of the photographs is

vital to the proper estimation of the design load.

Image analysis and image processing has been used widely in the biological science literature

and many of the techniques used to filter and process images have arisen from these fields.

Similarities between particles and cells and the ability to capture real time images have led to

explosion of its applications in particle engineering systems such as fluidised beds. In the last

decade, there has been substantial increase in the number of publications in image analysis of

particle/solid behaviour. An ISI web knowledge search (Engineering) using terms image analysis

and particles shows an increase from 57 articles in 2001 to 143 articles in 2010. Examples of

studies demonstrating the use of image analysis to resolve critical engineering problems include

Heffels et al. (1996), Obadiat et al. (1998), and Boerefijn and Ghadiri (1998). Dagot et al. (2001)

used image analysis to confirm the assumption that there is a decrease in the quantity or quality

of filamentous bacteria in a Sequencing Batch Reactor (SBR). The study concluded that image

analysis can be used to control and monitor the SBR in real time. Poletto et al. (1995) used image

analysis to establish a linear correlation between voidage pixel intensity within a fluidised bed.

46

Boerefijn and Ghadiri (1998) developed an image analysis technique to characterise particle flow

behaviour for fluidised bed jets. In another study, image analysis was used to describe particle

curtain behaviour in a solar particle receiver (Kim et al., 2009). Their study showed variation in

the solid volume fraction and the falling particle velocity at different heights within the curtain. It

can be concluded that image analysis is a powerful tool for solving different engineering

challenges in particle technology.

Image analysis is the process of extracting important information from images; mainly from

digital images by means of digital image processing techniques. An image can be defined as a

two-dimensional function, f(x, y), where x and y are plane coordinates and the magnitude of f at

any pair of coordinates (x,y) is called the pixel intensity of the image at that location.

There are four basic types of images, namely: binary, grayscale, true-colour or red-green-blue

(RGB) and indexed. In binary images, the pixels are either black or white and they are

represented as 0 and 1 for black and white respectively. The grayscale image consists of shades

of gray and the pixels range from 0 (black) to 255 (white). This type of image is predominantly

used in image analysis for engineering applications due to its distinctive and easily analysed

colour variation. For the true colour image, each pixel has a colour which is described by the

amount of red, green, and blue in it. Each of these components can have range of values from 0

to 255 giving a total of 2553 different possible colours in the image and every pixel in the image

corresponds to three values, complicating analysis. An indexed image has each pixel with a value

that does not give its colour but an index to the colour in an associated colour map. The

knowledge of the types of images facilitates appropriate choice of image analysis technique to be

implemented.

47

Different image analysis techniques are available in engineering applications and they are mostly

implemented using image processing software. These techniques can be sub-categorised into the

following algorithms: image enhancement, image restoration and image segmentation. Image

enhancement can be regarded as the pre-processing of an image and involves the sharpening of

the image, highlighting the edges, improving image contrast or brightness. The next step in the

algorithm is the image restoration and it entails repairing the damage done to an image by a

known cause. Examples of image restoration are removal of optical distortions or periodic

interference. The image segmentation involves isolating certain regions of interest within the

image or subdividing the image into component parts. This process can include estimating the

area within the region of interest or finding and counting particular shapes in the image. Figure

4.1 shows a typical algorithm structure used in image processing.

48

Figure 4.1: Algorithm for image analysis

No

Acquire the

image

Is pre-

processing

required?

Image

enhancement

Is image

damaged?

Image

restoration

Any regions of

interest in the

image?

No

Image

segmentation

Output image or

data processing

No

Yes

Yes

Yes

49

4.1 Experimental set-up

A series of experiments were carried out at pilot scale in order to determine dryer design

loadings. The experimental conditions examined in this study are stated in Table 4.1. The

flighted rotary dryer used in the experiments is rotated in a clockwise direction and aligned to be

perfectly horizontal. The geometrical configuration of the dryer is described in Table 4.2 and a

diagram defining the flight geometry is provided in Figure 4.2. Figure 4.2 illustrates a typical

two-staged flight defined by the flight base length (s1), flight tip length (s2), the angle between

the flight base and the drum wall (α1) and angle between the flight segments (α2). A camera on a

tripod stand was placed 1.5 metres in front of the end of the drum and positioned around the 9

o'clock axis of the drum, so as to minimise parallax error. The photographs were taken using a

Nikon D80 camera which was adjusted to manual focus settings with focal length of 18 mm and

aperture size of 3.5. The shutter speed was 1/60 second. The images were taken using the

continuous operation mode and in grayscale (2592 x 3872 pixels). Six 500 watt spotlights on

tripod stands were placed to illuminate the drum cross section. The laboratory room was

blackened so as to reduce variation in the ambient light. A polished Perspex plate with a 5 mm

thickness was used on the front end of the dryer and a black screen was used on the back end of

the dryer throughout the experiment. The built-in flash system of the camera could not be used

because of its reflective effect on the Perspex front end of the drum.

50

Table 4.1: Operating conditions for the design load experiments

Experimental conditions

Material Filter sand

Rotational speed 2.5 rpm, 3.5 rpm and 4.5 rpm

Moisture content

0.4 wt% fluid content sand




Table 4.2: Experimental set up and geometrical configuration of the drum

Parameter Value

Length of dryer (L) 1.150 m

Diameter of dryer (D) 0.750 m

Flight base length (s1) 0.033 m

Flight tip length (s2) 0.030 m

Flight base angle (α1) 90 o

Flight tip angle (α2) 124 o

Flight thickness 0.002 m

Number of flights 24

Figure 4.2: Schematic diagram of the flight geometry

4.1.1 Material and its properties

Filter sand was sieved, washed and dried in the oven for 12 hours prior to loading. Pretreatment

of the filter sand was necessary to remove fine particles which, because of electrostatic

interference, obscured the cross

sand was determined using sieves and the average particle size of the treated filter sand was 300

µm. Low volatility Dow Corning 200 fluid, 350CS (laboratory grade) within the range of 0.4

wt% to 2.1 wt% was added to the filter sand so as to investigate the effect of fluid content or

solids cohesion on design load. Small quantities of low volatility Dow corning fluid can be used

to carefully alter the angle of repose of the solids without e

However, un-wetted filter sand was not used because of the electrostatic obscuration due to dust

particles abraded during an experiment. The characteristics of the filter sand with different fluid

contents are outlined in Table

index (ffc) and is the ratio of consolidation stress and unconfined yield streng

measured using a ring shear tester. The loose bulk density was determined in the laboratory by

: Schematic diagram of the flight geometry

its properties



interference, obscured the cross-sectional photographs. The particle size distribution of the filter



wt% was added to the filter sand so as to investigate the effect of fluid content or


to carefully alter the angle of repose of the solids without evaporating during the experiments.

wetted filter sand was not used because of the electrostatic obscuration due to dust


Table 4.3. The free-flowing characteristic was described by the flow

) and is the ratio of consolidation stress and unconfined yield streng


51



sectional photographs. The particle size distribution of the filter



wt% was added to the filter sand so as to investigate the effect of fluid content or


vaporating during the experiments.

wetted filter sand was not used because of the electrostatic obscuration due to dust


flowing characteristic was described by the flow

) and is the ratio of consolidation stress and unconfined yield strength, which was


52

pouring the material into an empty 200ml volumetric cylinder. The consolidated density was

determined by tapping the sides of the cylinder until no more consolidation occurred. The

samples were weighed to determine the consolidated density. Density measurements were

repeated five times to determine the average value and the standard deviations. The effect of

fluid content on the bulk density and the free-flowing nature of the sand was significant. Care

was taken prior to each experimental run to ensure even solids distribution along the drum

length.

Table 4.3: Characteristics of the material at different moisture content

Fluid content (%wt) Flow index (ffc) Loose Bulk density

(kg/m3)

Consolidated Bulk

density (kg/m3)

0.40 11 1406 ± 8 1559 ± 13

0.75

1.25

6

3.7

1374 ± 10

1326 ± 14

1560 ± 15

1564 ±15

2.10 2.2 1262 ± 14 1537 ± 20

4.2 Image segmentation and manual analysis

Previous studies have used ImageJ software to manually determine the area of solid within the

flights (Christensen, 2008) and to measure angle of repose (Lee, 2008; Lee & Sheehan, 2010). In

the manual process, ImageJ software is used to trace regions of interest such as the boundaries

defining the enclosed area within a flight (see Figure 4.3) and computing the enclosed area. The

photographs were scaled in ImageJ to determine the length of a pixel and the in-built area

function was used to determine the cross-sectional area of both flight-borne solids and airborne

solids. The scaling process involved using the diameter of the dryer (75 cm) as the reference

length. Computed areas were segmented into four regions of interest. These regions are the First

Unloading Flight (FUF), flight

in lower half of the drum (LHD)

any solids within the circle enscribed by the flight tips. These regions are pictorially described in

Figure 4.3 and defined in Table

(γ +θ), the LHD area lies within the range of angle (

(γ). Manual use of ImageJ software is a good a

determine the boundary of solid

is that it is very time consuming to analy

(a)

Figure 4.3: Drum cross section including the angles used to define the regions of interest for

the Image segmentation.


Unloading Flight (FUF), flight-borne solids in upper half of the drum (UHD), flight

in lower half of the drum (LHD), and airborne solids in the free-falling curtains (AP) defined as


Table 4.4. In Figure 4.3a, the UHD area lies within the range of angle

, the LHD area lies within the range of angle (β) and the FUF lies within the range of angle

. Manual use of ImageJ software is a good analytical tool which enables intuition to be used to

solid within the flights. However, a major limitation of manual tracing

is that it is very time consuming to analyse multiple photographs.

: Drum cross section including the angles used to define the regions of interest for

53


borne solids in upper half of the drum (UHD), flight-borne solids

falling curtains (AP) defined as


, the UHD area lies within the range of angle

) and the FUF lies within the range of angle

nalytical tool which enables intuition to be used to

within the flights. However, a major limitation of manual tracing

(b)

: Drum cross section including the angles used to define the regions of interest for

54

Table 4.4: Regions of interest corresponding to Figure 4.3

Region of interest Location

FUF γ

UHD γ + θ

LHD β

4.2.1 Image enhancement

In view of the thousands of photographs analysed, this study developed an automated process for

computing the cross-sectional area of solids in the regions of interest for batches of photographs.

A number of approaches using MATLAB and ImageJ were tested and compared to manual

tracing to assess their accuracy. The initial MATLAB process involved cropping the image and

counting the total number of pixels in the region of interest to estimate the area. The cropping

process required removing the airborne solids (AP) from the image and also excluding the

background by cropping the edges of the drum. The cropped image contained the solid retained

in the flights as well as the voids between the flights. The MATLAB calculation entailed

determining the pixel intensity cut-off point for the entire image. The concept of pixel intensity

cut-off, also referred to as thresholding, was to remove pixel values of the flight components and

voids, thereby retaining only solid within the flight. To determine the exact minimum brightness

value (Bmin) or cut-off point for the region of interest, matrix indexing was done. The matrix

indexing gave an insight into the exact brightness value within the region of interest. It was

observed that portions of solid within the flight had the same pixel value as the flight

components, and appropriate Bmin values differed between the upper and lower half of the drum

due to subtle variation in lighting. Camera location also led to unavoidable difficulties in

55

determining the edges of the flight-borne solids in the bottom half of the drum due to parallax. It

is interesting to note that the naked eye can discern subtle differences making manual tracing

more reliable. The results presented in Tables 4.5 and 4.6 demonstrate the inconsistency in the

approach and the overestimation of the region of interest and provide justification for both image

enhancement and segmentation.


32 kg loading condition)

Technique Area at FUF

(cm2)

Area of UHD

(cm2)

Area of UHD

+ LHD (cm2)

ImageJ manual calculation 26.00 102.47 220.74

MATLAB calculation 29.08 125.34 259.95




(cm2)

Area of UHD

(cm2)

Area of UHD

+ LHD (cm2)


MATLAB calculation 28.80 103.68 258.53

Further investigation observed variation in the brightness and contrast properties within images

of the same experimental run. The variation in the brightness properties could be attributed to

experimental conditions such as fluctuation in the lightning set-up. Image enhancement

techniques used to overcome these issues are discussed in the following section.

56

4.2.1.1 Filtering and thresholding in ImageJ software

The images were filtered in batches using ImageJ software prior to the processing for the cross-

sectional area in MATLAB. The filtering macro was developed in ImageJ and the three-step

process involved adjusting the brightness/contrast of the image, the smoothing and edge

enhancement of the pixels of the bulk solid within the flight, followed by thresholding. The

brightness/contrast of the image was adjusted by increasing the brightness/contrast using the in-

built ImageJ function. The smoothing filter (ImageJ plugin) was based on the sigma probability

of the Gaussian distribution and was defined by the parameters outlined in Table 4.7. The sigma

filter smoothes the image noise by averaging only those neighbourhood pixels which have

intensities within a fixed sigma range of the centre pixel (ImageJ plugins, 2007). In this way,

image edges are preserved, and subtle details within the image are maintained. The next process

in the developed macro was the thresholding of the image. An example of a filtered and

thresholded image is presented in Figure 4.4. The thresholding values of the upper and lower

halves were different due to subtle contrast difference arising from spotlight location. The

developed macro was implemented across the stack of images for a particular experimental

condition. The thresholding reduced the longitudinal background effect of the drum by turning

every pixel value within the background to black (zero pixel value). The regions of interest

within the flights were the non-zero pixel values.

Table 4.7: Values for the thresholding process

Filtering and thresholding

process

Brightness and contrast value

Sigma filtering

Thresholding value

(a) Original image example (b) Filtered image example

Figure 4.4: Original and filtered images in ImageJ software

: Values for the thresholding process

Filtering and thresholding Upper half of

the drum (αααα +θθθθ)

Lower half of the drum

140

Radius = 4, use = 3,

minimum = 1


minimum = 0.9

168

Original image example (b) Filtered image example

: Original and filtered images in ImageJ software (upper half filter)

57

Lower half of the drum

(ββββ)

160


minimum = 0.9

177

Original image example (b) Filtered image example

(upper half filter)

58

4.3 Validation of image analysis

In order to validate the image processing techniques, five photographs at different loading

conditions of 0.4 wt% fluid content experimental run were analysed manually and averages

calculated. The comparisons between techniques are presented in Tables 4.8- 4.10.

The combined ImageJ enhancement and MATLAB calculation technique slightly over-estimated

the area when compared with ImageJ manual calculation. The deviation was attributed to the

presence of solid stuck to corners and surface junctions between flights, which have high degree

of pixel intensity but are excluded in the manual calculation because of intuition elimination. The

discrepancies in the results are found to be consistent for different loading conditions and thus

introduced an assumed consistent bias in the data, which makes it appropriate for analysis of

design loading. A t-test at 95% confidence interval was performed and indicated that for the

FUF, the ImageJ manually calculated approach and the combined ImageJ enhancement and

MATLAB approach are equivalent. The automated combined ImageJ enhancement and

MATLAB calculation technique was used to process the remaining photographs. MATLAB code

is presented in Appendix C.




(cm2)

Area of UHD

(cm2)

Area of TP

(cm2)

ImageJ enhancement and MATLAB calculation 27.32 93.48 234.07


59




(cm2)

Area of UHD

(cm2)

Area of TP

(cm2)



Table 4.10: Comparative estimation of regions of interest (4.5 rpm, 0.4 wt% moisture

content, 34.5kg loading condition)


(cm2)

Area of UHD

(cm2)

Area of TP

(cm2)



4.4 Estimation of design load

Matchett and Baker (1988) established a criterion to estimate the design load experimentally.

They observed a change in the slope of the plot of holdup versus feed rate (Figure 4.5). Their

study concluded that the change in slope indicated a transition from under-loaded to over-loaded

conditions and the transition point was regarded as the design load. Their study also observed

saturation of mass within the airborne phase at design loading.

60

Figure 4.5: Plot of holdup against feed rate (Matchett & Baker, 1988)

In line with the Matchett and Baker (1988) concept of saturation, four different approaches were

considered in this study: visual analysis, change in gradient with respect to loading of flight-

borne solids, saturation of the airborne solids, saturation of the upper flight-borne solids, and

saturation of the FUF. The concept of these approaches is discussed in subsequent sections.

4.4.1 Visual analysis approach

The visual analysis approach involved examining all the photographs at different loading

conditions to determine the loading at which there is discharge of solids at precisely the 9

o’clock position as shown in Figure 2.1b. However, because of the fluctuating nature of flight

loading, the visual approach gave a range of design load conditions for the set of photographs

and is excessively time consuming. It assumed that the design load lies between the loading

condition when the discharge was first observed and the next loading condition. This approach

may not be suitable for high moisture content solids because of its avalanche discharge pattern as

61

the drum rotates. Hence, the visual analysis was not considered appropriate to determine the

design loading.

4.4.2 Change in gradient of total flight-borne solids

The total flight-borne solids was estimated by summing the areas of flight-borne solids in both

the upper half of the drum (UHD) and the lower half of the drum (LHD). Figure 4.6 shows the

increase in the total flight-borne solids as the loading condition increases. Qualitatively, it was

evident that there is a change in the slope as the loading condition passes a certain point.

However, it is difficult to determine the exact loading condition where the gradient changes.

Piecewise regression analysis was carried out on the data but is subject to considerable error as a

result of the uncertainty in the gradient past the design point.

Figure 4.6: Total passive (UHD + LHD) versus loading for 0.4 wt% moisture content solids

at 3.5 rpm

5

55

105

155

205

255

305

355

10 20 30 40 50 60

To

tal

pass

ive

(cm

2)

Loading condition (kg)

62

4.4.3 Saturation of the airborne solids and of the flight-borne solids in the upper half of

the drum

Prior to the estimation of the area covered by airborne solids, the image enhancement technique

described in section 4.2.1.1 was implemented across the stack of images using threshold values

of 104 and 120 for the upper half airborne solids and the lower half airborne solids of the drum

respectively. The drum was segmented by excluding anything outside the radius defined by the

flight tips. The percentage coverage by the airborne solids was determined using Equation 4.1.

The flight tip radius was calculated as 0.3262 metres using Lee and Sheehan (2010) geometric

model.

��v x� �x�� = ��v x� �x�� G v��x�� wxy��w��v x� ?ℎ� �@5 �x@�� G ?ℎ� �y��ℎ? ?��w × 100% 4.1

Figure 4.7 shows the percentage coverage by the airborne solids (AP) and the area of the flight-

borne solids in the upper half of the drum (UHD) at different loading conditions. It is interesting

to note that the profiles of both areas with respect to loading are independently very similar. The

peaks in the graphs can be regarded as the point where there is maximum interaction between

solids and gas. They may also be considered to be the transition point from under-loaded to

overloaded, i.e. the design load. It can be seen there was a relative saturation in the areas in the

later stages of loading after this transition point. At this stage, the reason for the peak in the UHD

and AP, repeatable at different rotational speeds, is unclear. Variation in both the consolidated

density within the flights and solids voidage within the falling curtains may contribute to this

phenomenon and will be the subject of further investigation. The standard deviations for the

areas of flight-borne solids in UHD are high and the complexity of determining the solids

63

voidage of the airborne solids propagated errors and could introduce significant bias in

estimation of the design load. Using the peak in the approaches to quantity design load relies on

the accuracy of individual data points.

Figure 4.7: Saturation of the airborne solids and flight-borne solids in the upper half of the

drum (3.5 rpm)

4.4.4 Saturation of the First Unloading Flight (FUF)

The study assumed that the design load was achieved when the mass at FUF was at maximum

capacity, i.e. saturated. This relies on the assumption that the flight-borne mass becomes constant

when the dryer is over loaded. Under this assumption, the average area in the FUF from each

experimental run was plotted against loading as shown in Figure 4.8 (a-c). The shape language

modelling (SLM) technique developed by D’Errico (2009) was used in the regression of

piecewise functions to these data sets. The SLM approach is based on least squares splines

subjected to simple constraints. It should be noted that the right hand slope in the SLM approach

0

20

40

60

80

100

120

0

10

20

30

40

50

0 10 20 30 40 50 60

Are

a o

f th

e fl

igh

t-b

orn

e so

lid

s in

th

e

up

per

ha

lf (

cm2)

Per

cen

tage

of

are

a o

f co

ver

ed b

y t

he

air

born

e so

lid

s


Airborne solids Flight borne solids in UHD

64

was constrained to zero (assumed saturation) and the left hand line was constrained to be linear

but not constrained to pass through the origin. The discontinuity/break location along the curve

indicates the estimated design load. This approach offers significant advantage with respect to

quantification of experimental error when compared to the change in gradient approach

described in section 4.4.2. The SLM fitting technique was implemented in the MATLAB

Optimization Toolbox (see Appendix D for the user-defined part of the MATLAB code). It can

also be seen from the graphs that relatively constant FUF area values were achieved from the

design load to the overloading condition. The results for the FUF data and the calculated design

loadings are presented in Table 4.11. Confidence intervals were determined via rules of

propagation of errors (Harrison & Tamaschke, 1984; Oosterbaan et al., 1990). The detailed

process of estimating the confidence intervals is presented in Appendix E.

(a)

0

10

20

30

0 10 20 30 40 50 60

Are

a a

t F

UF

(cm

2)


65

(b)

(c)

Figure 4.8: Design load of (a) low (0.75 wt% 2.5 rpm, 0.4 wt% (3.5 rpm and 4.5 rpm)), (b)

medium (1.25 wt%) and (c) high (2.1 wt%) moisture content solids at different rotational

speeds

0

10

20

30

40

15 20 25 30 35 40 45 50

Are

a a

t F

UF

(cm

2)


0

10

20

30

40

50

20 25 30 35 40 45 50 55

Are

a a

t F

UF

(cm

2)


2.5 rpm Experiment 3.5 rpm Experiment 4.5 rpm Experiment

2.5 rpm Fitted 3.5 rpm Fitted 4.5 rpm Fitted

66

Table 4.11: Design load based on constant area at FUF (at different experimental conditions)

Rotational

speed (rpm)

Moisture content

(wt%)

Dynamic angle

of repose ( degrees )

Design Load

(kg)

Area at FUF

(cm2)

2.5

0.75 46.7 ± 2.9 33.9 ± 7.7 27.3 ± 0.92

1.25 51.1 ± 1.6 38.4 ± 4.8 35.6 ± 0.43

2.10 58.3 ± 2.3 45.5 ± 8.1 42.9 ± 0.60

3.5

0.40 44.7 ± 2.0 31.8 ± 3.7 27.9 ± 0.47

1.25 54.3 ± 2.6 40.8 ± 4.4 37.3 ± 0.34

2.10 59.4 ± 1.7 50.3 ± 8.0 42.3 ± 1.00

4.5

0.40 45.0 ± 2.5 34.7 ± 4.4 29.0 ± 0.53

1.25 56.7 ± 2.4 42.7 ± 4.6 37.2 ± 0.32

2.10 62.3 ± 2.8 54.3 ± 5.3 44.5 ± 0.71

Rotational speed had significant effect on the design load of the dryer as observed in the results

presented above. This can be attributed to a number of factors. Increased rotational speed leads

to an increase in the dynamic angle of repose of the solids and a potential increase in the bulk

density of the flight-borne solids. Higher rotational speeds also lead to an increased rate of

discharge of solids into the airborne phase which increases the total dryer holdup. This is further

supported by the observed decrease (with respect to rotational speed) in the gradient of the area

versus load line, particularly evident in Figure 4.8(b). The relationship between rotational speed

67

and angle of repose has been presented in Schofield and Glikin (1962). Fluid content or level of

cohesion has a significant effect on the design load of the drum. As the fluid content of the sand

material increases, its cohesive nature increases and thus increases the angle of repose of the

material within the flights.

The design loading at 3.5 rpm for example, showed increasing uncertainty as the fluid content or

cohesion increases (3.7 kg to 4.8 kg to 8.0 kg). This was attributed to the avalanching flow

behaviour of the more cohesive material as it discharges from the flight, and the resultant

increase in scatter of the measured data points. Similar discontinuous discharging patterns were

observed in the flight unloading experiments described in Lee and Sheehan (2010). Additionally,

in the cohesive solids loading experiments, the solids tended to adhere to the Perspex plate in the

small junctions and spaces around the flights, which reduced the quality of the processed images.

Qualitative observations of the images of airborne solids from the cohesive solids loading

experiments were substantially different to those observed using free-flowing solids. The widths

of the free-falling curtains were considerably narrower for the cohesive solids compared to the

particle curtains in the free-flowing solids experiments, as demonstrated in Figure 4.9. This

indicates that the density and flow development of the particle curtains are not comparable, and

in the cohesive system significant clumping of solids was observed. This clumping behaviour has

also been observed in industrial raw sugar flighted rotary dryers (Britton et al., 2006).

68

(a) Low moisture content (0.4%) (b) High moisture content (2.1%)

Figure 4.9: Variation in the cropped image pixel intensity for free-flowing and cohesive

falling particle curtains (3.5 rpm)

4.5 Estimation of the airborne solids

The amount of solids within the airborne or active phase is important to accurate determination

of the total dryer holdup and is also an important property in flighted rotary dryer solid transport

modelling. In addition, proper understanding of the exact amount of solid in contact with the

drying gas is important to ascertain the efficiency of interaction between the gas and solids

within the dryer. In determining the airborne solids, different approaches were considered. The

first approach involved subtracting the total passive (TP), which is the mass of flight-borne

solids during rotation, from the total mass within the drum which can be determined by stopping

the dryer and collecting photographic images of the cross section. The deficiency of this

approach is the high degree of sensitivity of the difference in masses to the accurate

determination of the bulk density of the solids in the flights during drum rotation. In this study,

the laboratory-determined consolidated bulk density of the solids was assumed to be the bulk

density of the solids within the rotating flights, which over-estimated the passive mass in

69

comparison to the total mass and led to unrealistic masses for the airborne solids. An alternative

approach was to estimate the airborne solids by manually tracing the area covered by falling

particle curtains within each photograph (see Figure 4.10 for example). Consequently, a method

to determine the solids voidage within the falling particle curtain was required. Computational

Fluid Dynamics (CFD) was used to facilitate calculation of the solid volume fraction in the

cascaded solid.

Figure 4.10: The manually traced falling curtains

Previous studies have modelled gas-solid interaction and particle curtain behaviour using CFD

(Wardjiman et al., 2008; Kim et al., 2009; Wardjiman et al., 2009). CFD involves the numerical

solution of mass, momentum and energy conservation equations in the flow system of interest.

The two most common approaches to modelling this type of multiphase flow are Eulerian-

Eulerian and Eulerian-Lagrangian models. The Eulerian-Langrangian method provides a direct

physical interpretation of particle-particle and particle-wall interactions but requires large

70

computational capacity to simulate the enormous numbers of particles simultaneously. In the

Eulerian-Eulerian approach, both phases are treated as interpenetrating continua, and therefore

this approach has less computing requirement than Langrangian approach. Both 2D (Kim et al.,

2009) and 3D (Wardjiman et al., 2009) Eulerian-Eulerian approaches have been successfully

used to model voidage and shape of free-falling particle curtains.

The governing equations for the Eulerian-Eulerian approach are presented below. The standard

k-ε turbulence model was used and the conservation equations for the solid phases were based on

the kinetic theory for granular flow.

The continuity equation for each phase (k = g, s) can be stated as:

h�LVTV�h? + ∇. �LVTVAV� = 0 4.2

The momentum balance for gas phase is:

h�L3T3A3�h? + ∇. �L3T3A3A3� = −L3∇< − ∇. �L3Z3� + L3T3�� + M�A3 − A�� 4.3

The momentum balance for solid phase can be written as:

h�L�T�A��h? + ∇. �L�T�A�A�� = −L�∇< − ∇. �L�Z�� + L�T�� + M�A� − A3� 4.4

whereα, ρ, U, P and g are the volume fraction, density, velocity vector, pressure and gravity

respectively. The term M is the interphase transfer coefficient which can be computed from the

drag coefficient, the Reynolds number and the solids volume fraction.

M is expressed as:

M = 34 �P L�L3T3�� A3 − A��L3��.�� 4.5

71

The drag coefficient was evaluated using the commonly used Schiller−Naumann (1935) drag

correlation stated in Equation 4.6.

( )

>

<+

<

=

1000 Re 44.0

1000Re Re15.01Re

24

0.2 Re Re

24

687.0

DC

4.6

The granular kinetic theory based models introduce several additional terms in the solid stresses,

which in turn modify momentum conservation equations for solid phases.

The solid stress for the solid phase can be written as:

L�Z�� = −<�4 � + 2L�S� � + L� `R� − 23 S�c ∇. A�4 � 4.7

where Ps is the solids pressure, µs is the solids (shear) viscosity, and λs is the solids bulk

viscosity. S is given by:

� = 12 �∇A� + �∇A��8� 4.8

In the literature, several different expressions have been derived for solids pressure, solids shear

viscosity and solids bulk viscosity by employing different approximations and assumptions while

applying the kinetic theory of granular flows. The constitutive equations used in this study were

as follows:

The total solid shear viscosity was expressed as follows (Lun et al., 1984):

S� = 45 L�T��1 + �� `O�� c� �� 4.9

The solids pressure, Ps is:

<� = L�T�O��1 + 2�1 + ��L�� 4.10

72

where es is the value of the restitution coefficient of solid particles, g0s is a radial distribution

function and θs is the granular temperature which was defined via:

O� = 13 @"� 4.11

The radial distribution can be seen as a measure of the probability of inter-particle contact and

was described using the Gidaspow (1994) correlation:

�� = 35 �1 − ` L�L� 1(�c�� 4.12

L� 1(� = 0.62

The turbulence effect of the solid phase was estimated using the zero equation turbulence model.

On the other hand, the eddy viscosity in the stress tensor of the gas phase was estimated using

Equation 4.13. It contains two unknown variables, k and ε, which refer to turbulent kinetic

energy and turbulent energy dissipation rate. Previous studies in gas-solids interaction modelling

have found the standard 2 − N model to be suitable in modelling turbulence in the continuous

(gas) phase in free-falling particle curtains (Koksal & Hamdullahpur, 2005; Wardjiman et al.,

2008; Wardjiman et al., 2009). Consequently, the turbulence prediction of the gas phase was

obtained using the standard 2 − N model.

S& = T�� 2�N 4.13

Turbulence kinetic energy was determined via:

T h2hj" = S& �h@��hj" + h@Q�hjC � h@��hj" + hhj" �` SUVc h2hj"� − TN 4.14

The turbulent energy dissipation rate was determined via:

73

T hNhj" = �� N2 S& �h@��hj" + h@Q�hjC � h@��hj" + hhj" �` SU�c hNhj"� − ��T N�2 4.15

�� = 1.44, �� = 1.92, �� = 0.92, UV = 1, U� = 1.3

4.5.1 Vessel geometry and grid generation

In this study, the modelled curtain was the discharging flight at an angular position of 150o

within the pilot scale rotary dryer (Figure 4.11). This location was selected for two reasons: the

150o curtain was the best centred falling solid with respect to the image orientation and

geometrical calculations showed the 150o curtain to provide an average mass flow rate, with

respect to rotation. Geometric calculations based on the experimentally observed dynamic angle

of repose, measured at the 9 o'clock position, were performed using the model described in Lee

and Sheehan (2010). The mass flow rate profiles across the entire range of rotational angles that

were generated using this model are presented in Figure 4.12 and show the mass flow rate at

angular position of 150o to be a reasonable representation of the average flow rate of the flights.

Experimentally measured and geometrically derived model inputs are outlined in Table 4.12.

74

(a) Original image (b) Colour map of cropped original image

(coloured by pixel intensity)

Figure 4.11: Experimental images of the discharged solid at angular position of 150o

Figure 4.12: Geometrically calculated flight discharge mass flow rate profiles at varying

rotational speed

75

Table 4.12: Experimental conditions for the 150o free-falling particle curtain

Parameters 2.5 rpm 3.5 rpm 4.5 rpm

Mass flow rate (modelled) 0.073 kg/s 0.103 kg/s 0.134 kg/s

Bulk density 1361 kg/m3 1361 kg/m3 1361 kg/m3

Particle density 2630 kg/m3 2630 kg/m3 2630 kg/m3

Particle size 300 µm 300 µm 300 µm

Dynamic angle of repose* 46.9o 44.7 o 45.0o

Width of discharged solid at the flight tip 0.006 m 0.006 m 0.006 m

Vertical height of curtain 0.59 m 0.59 m 0.59 m

Modelled curtain depth 0.15 m 0.15 m 0.15 m

The schematic diagram of the three-dimensional CFD model is shown in Figure 4.13. The

commercial grid generation package (ANSYS Inc.) was used to create body-fitted, structured

grid nodes for the geometry studied.

76

Figure 4.13: Schematic diagram of the CFD model

4.5.2 Boundary conditions

The input values for the CFD analysis were the experimental and modelled conditions outlined in

Table 4.12, determined from images of a design loaded dryer and via the geometry model. The

inlet solid volume fraction was specified as a function of particle density and bulk density as

shown in Equation 4.16. The gas inlet and outlet were modelled as opening boundary conditions.

The reference pressure of zero Pa was specified and the speed of the air phase was zero. The

solid inlet was modelled as inlet only. The other parts of the geometry were modelled as walls,

and a ‘no slip’ boundary condition was specified for the vessel walls.

Tu = T�&�1 − N � 4.16

where Tu, T�&, N are the bulk density, particle density and voidage.

4.5.3 Simulation

The solving of the Eulerian-Eulerian equations was done on a Pentium 4, 2GB RAM, 1.86 GHz

PC. The average computing time was approximately one hour and thirty minutes for each run. A

high resolution discretisation scheme was used for all the equations in the study. In the analysis,

77

a solution was considered to have converged when the total normalised residual for the

continuity equation dropped below 1 x 10-4.

4.5.4 Results and Discussion

Preliminary runs were carried out for the geometry to ensure the solutions were independent of

grid size. The results revealed that the differences in mean solid volume fraction were negligible,

between 223,200 cells and 438,900 cells. The cut-off point for defining the curtain edge was

taken to be a solids volume fraction of 1 x10-5 (Lee, 2008; Wardjiman et al., 2009). Referring to

Figure 4.13, solid volume fractions were extracted from the xy plane through the middle of the

box (z=0.15m). An example of this plane is shown in Figure 4.14. Solids volume fraction was

averaged across a line in the x direction and within the curtain edges for a range of vertical

heights. These results are presented in Table 4.13.

Figure 4.14: Contour profile of the solid volume fraction

The solid volume fraction contour profile presented in Figure 4.14 was compared with the cross-

sectional photograph taken during the equivalent experiment such as that shown in Figure

78

4.11(a). For comparison, Figures 4.15 and 4.16 show the area profiles of the pixel intensity and

solid volume fraction in the experimental image and the CFD respectively, which are

qualitatively well matched. Taking the average area by integration of area profiles, both graphs

gave the same area of 0.0278 m2, illustrating similarity between the CFD profile and the image

profile. The pixel intensities within the curtains in the photographic images reduce with vertical

distance of the curtain as illustrated qualitatively in Figure 4.11(b) and quantitatively in Table

4.13. A comparable reduction in solid volume fraction was observed in the CFD results as well.

However, contrary to expectations (Poletto et al., 1995) a linear correlation between the pixel

intensity of the image and voidage could not be established across the entire range of volume

fractions. At low solids volume fraction (<0.003) a direct correlation between volume fraction

and pixel intensity was observed. However, at higher solids volume fractions the image pixel

intensity becomes saturated. Pixel saturation is a result of both high volume fraction and also the

significant depth (1.15 m) of curtain being photographed. If a significantly reduced depth of field

was used, then the approach described in Nopharantana et al. (2003) may be applicable. In this

approach, thresholding could be used to determine area fractions covered by the particles and

then converted into volume fraction. However, a depth of field in the range of 10mm would be

required. Unfortunately wall effects would also be more significant in this experimental setup.

79

Figure 4.15: Area covered by the threshold values within the original image (0.4 wt%, 4.5

rpm)

Figure 4.16: Area with CFD contour profiles, which are defined by their solid volume

fraction

0

0.0001

0.0002

0.0003

0.0004

0.0005

115

119

123

128

133

138

143

148

153

158

163

168

173

178

183

188

193

198

203

208

213

218

223

228

233

Are

a c

ov

ered

by t

he

thre

sho

ld v

alu

e

(m2)

Threshold value

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

Are

a c

ov

ered

by

th

e co

nto

ur

(m2)

Solid volume fraction ( x 1E-05)

80

Table 4.13: Threshold value and solid volume fraction

Position from the solid inlet (m) 0.1180 0.1967 0.2950 0.3933 0.4720

Average image threshold value 189.9 183.0 182.2 172.8 169.1

Average CFD modelled Solid

volume fraction

0.2180 0.0043 0.0031 0.0026 0.0023

In order to combine CFD results with the experimental images, an area averaged solids volume

fraction (L�&) was obtained. Again referring to Figure 4.13, solid volume fractions were extracted

from the xy plane through the middle of the box (z=0.15 m). The solids volume fraction was

averaged across the entire particle curtain from the curtain entrance to a set distance below the

entrance (hct). These results are presented in Figure 4.17. By way of example, the average

volume fraction of solids within a curtain 50 cm long would be 0.0049. In order to use the CFD

results in combination with a matching experimental image, empirical equations for average

solids volume fractions versus curtain height were derived from the data sets in Figure 4.17, and

are presented in Table 4.14.

81

Figure 4.17: Effect of curtain height on solid volume fraction at different mass flow rates

(for free-flowing solids)

Table 4.14: Empirical equations for determining solids volume fraction (αct) within the

curtain as a function of curtain vertical drop distance in cm (hct) (for free-flowing solids)

Mass flow rate (kg/s) Empirical equations

0.073 L�& = 0.003043ℎ�& + 0.07083ℎ�& + 1.209

0.103 L�& = 0.002479ℎ�& + 0.1592ℎ�& + 2.065

0.134 L�& = 0.00237ℎ�& + 0.2236ℎ�& + 2.409

Within a flighted rotating dryer there are multiple curtains and the height of each curtain within

the drum varies according to flight location. In determining the mass of airborne solids, all

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 10 20 30 40 50 60

So

lid

volu

me

fra

ctio

n

Height of curtain (cm)

0.073 kg/s 0.103 kg/s 0.134 kg/s

82

curtains within a single experimental data set were assumed to be discharging solids at the

average mass flow rate determined via the geometry code. Curtain discharge rates are a complex

function of flight and drum geometry, and Figure 4.12 illustrates the profiles as a function of

rotational angle. Averaging is thought to be a reasonable simplification in line with the approach

taken in compartment process models of flighted rotary dryers such as those of Sheehan et al.

(2005) and Britton et al. (2006). The mass of solids in each curtain (5�&*) of length hct was

calculated using Equation 4.17, where Ac is the cross-sectional area of each curtain in an image

and L is the length of the dryer (1.15 m). The bulk density of each curtain (Tu�&) in Equation 4.17

was determined using Equation 4.16, where the voidage �N � was equal to �1 − L�&� and the

solids volume fraction �L�&� was calculated via the relationships described in Table 4.14.

5�&* = Tu�. × ��& × m 4.17

The total mass of the airborne phase (5() was estimated by summing the masses of all the

curtains contained in each image, via Equation 4.18, where nct is the total number of curtains.

5( = e 5�&*#�."�� 4.18

The estimated masses of airborne solids are presented in Table 4.15 for the low moisture content

experimental runs. The masses presented are the average from a selection of five images taken

from the batch of photos closest to the determined design loading state. Images were also

selected with the FUF as close as possible to the 9 o'clock position. It is noted that the proportion

of airborne solids in a design loaded dryer is not constant and increased with increasing

rotational speed. It is also well known that an increase in rotational speed reduces solids

residence time. Airborne masses for the higher moisture content solids were more problematic to

83

determine because of the cohesive nature of the solids and the complexity of modelling these

flows using CFD. CFD modelling of cohesive particle curtain flows was not attempted in this

work.

Table 4.15: Active phase for different angles of repose

Rotational

speed (rpm)

Moisture

content (wt%)

Dynamic angle of

repose (degrees)

Active

phase (kg)

Design

load (kg)

% active

phase

2.5 0.75 46.9 ± 2.9 1.4 33.9 4.0

3.5 0.40 44.7 ± 2.0 1.9 31.8 6.2

4.5 0.40 45.0 ± 2.5 2.4 34.7 7.2

4.6 Application of geometric modelling to predict design loading

The design loadings obtained experimentally were compared to predicted design loadings using

geometric models from the literature. The precise design loading condition was determined from

Figure 4.8(a-c) as described in the previous section. A selection of images was taken from the

batch of photos closest to the determined loading state and having the FUF tip closest to the 9

o'clock position. The total flight-borne holdup was estimated based on the average of the five

images selected from the set. ImageJ software was used to trace the regions of interest so as to

minimise potential errors in the validation process. Experimentally determined values for the

areas of the FUF and the UHD at design load were used in Equations 2.2 to 2.4. Table 4.16

presents the percentage of deviation of the model prediction from the experimental design

loading, based on area. The models suggested by Porter (1963) and Kelly (1977) overestimate

the design load and are less consistent (7.5% and 7.8% standard deviation respectively) when

compared to the predictions using the Baker (1988) model, which under-estimates the design

84

load but is more consistent (4.4% standard deviation). The propagated error in the validation

process was within 3%.

Table 4.16: Percentage of deviation of the design load model

Experimental conditions Experimental

Design load

(kg)

Percentage of model deviation

Solid

Rotational

speed (rpm)

Porter

(1963)

Kelly

(1977)

Baker

(1988)

0.4 wt% 3.5 31.5 37.8 43.5 -25.8

0.4 wt% 4.5 34.5 33.0 38.5 -31.5

0.75 wt% 2.5 33.9 24.3 29.5 -27.5

1.25 wt% 2.5 38 37.2 43.0 -21.3

1.25 wt% 3.5 41 22.3 27.3 -21.0

1.25 wt% 4.5 43 29.4 34.8 -19.3

2.1 wt% 2.5 43 20.1 25.1 -23.9

It is worth noting that Baker's model was based on the flight-borne mass only and excluded the

airborne solids. The relevant holdups for the other two models (Porter, 1963; and Kelly, 1977)

were not clearly defined in the original sources. In Table 4.16, these latter model predictions are

compared to the flight-borne solids only. In order to compare these model predictions against

total drum hold-up, two options were considered. The first involved determining the design

loading hold-up (for example, see Figure 4.8a). The cross-sectional area of the solid within the

drum was calculated by dividing the design loading mass by the solid consolidated density. The

second involved approximating the airborne hold-up from previous calculations (roughly 5–

10%). Using either of these approaches, the match of these models to the experimentally

85

observed design loadings still remains poor and they are also inconsistent across the spectrum of

experimental conditions. Based on the reasonable consistency of deviation in the results, a

correction factor which modifies Baker's (1988) model is recommended for modelling the flight-

borne solids in a design loaded dryer (Equation 4.19).

��w�� yxv��(��" 6 = �1.24 × 7)6�"3# � 4.19

where 7)6�"3# is given by Equation 2.4 and ��w�� yxv��(��" 6 is the design loading of the

passive or flight-borne solids.

The potential to use geometric modelling to determine airborne mass and thus develop predictive

models for the total flighted rotary dryer holdup was considered. The flighted rotary dryer

compartment model described in Britton et al. (2006) uses transport coefficients based on

average solids cycle times to determine the ratio of airborne to flight-borne solids. In their

model, transport coefficients regulating the flow between the airborne and flight-borne phases

were related to the mass averaged time for a solid particle to fall though the air phase (termed the

mass averaged fall time: maft) and the mass averaged time (tp) for the solid particle to return, via

flight rotation, back to the mass averaged discharge location (θD). The derivation of the mass

averaged discharge location (θD) via a flight discharge geometry model is described in Britton et

al. (2006) and Lee (2008).

Referring to Figure 4.18, the mass averaged falling height of a solid particle (mafh) can be

expressed as a function of the dryer radius (R) and the mass averaged discharge location

Equation 4.20. The first term in the right hand side of the equation represents the height when the

solid particle falls into the active phase (point i) to the tip of another flight at the base of the

86

drum (point ii) as shown in Figure 4.18 while the second term is the height from flight tip (point

ii) to the base of the drum (point iii). It should be noted that the derivation of the second term is

based on one’s judgment on where the particles should fall.

5v�ℎ = w��OP − 90$� × 2 × �\ + �`� + �\2 c − �\� 4.20

The mass averaged falling time (maft) of the solid can be calculated using Newton's equations of

motion (in this case neglecting drag and assuming that the initial velocity of the falling particle is

zero) via Equation 4.21, where �� is the acceleration due to gravity.

5v�? = �2 × 5v�ℎ�� 4.21

The time for a particle to return to the discharge point (tp) is a function of rotational speed (Y� in

radians per second and of the dryer geometry, such as the slope of the drum (θ ).

?� = v�xw �1 − `�5v�ℎ × �xw O��2 × �\� c Y

4.22

87

Figure 4.18: Drum cross section showing the mass averaged falling height geometrical

details

At steady state, the mass ratio of airborne (ma) to flight-borne (mp) solids at design loading can

be derived from a mass balance on the compartments within the model described in Britton et al.

(2006).

ℛ = 5v�??� = 5(5� 4.23

In Table 4.17, the ratios of the airborne to flight-borne solids based on the experimental images

coupled with CFD are compared to the ratios determined via the geometric modelling described

in Equations 4.20 to 4.23. Considering the propagated uncertainty in obtaining these ratios, the

results are in good agreement and demonstrate a very high degree of correlation (R2 ≈ 1).

Enhancing the quality of the geometric modelling with more realistic values, such as non-zero

iii

RF

900 2700

mafh

θD

i

ii

88

initial velocity and a reduced mafh to account for contact with flight-borne solids, would only

improve the match between these ratios.

Table 4.17: Ratio of airborne to flight-borne solids at design loading (with different angles

of repose)

Rotational

speed (rpm)

Dynamic angle of

repose (degrees )

CFD

approach

Geometric

model

2.5 46.9 ± 2.9 0.042 0.047

3.5 44.7 ± 2.0 0.064 0.067

4.5 45.0 ± 2.5 0.078 0.085

It is suggested that total dryer holdup under design loading (7)6�"3#898 ) can be determined using a

geometric flight unloading model, such as described in Britton et al. (2006), Lee (2008), Lee and

Sheehan (2010). Equation 4.19 can be used to determine the total flight-borne solids and the ratio

of cycle times in Equation 4.23 can be used to determine the airborne solids. Combining these

two holdup phases, the total holdup can be expressed as:

7)6�"3#898 = d1.24 d2 × e 5"#; f − 5\]\f �1 + ℛ� 4.24

4.7 Summary

The design loading for a pilot scale flighted rotary dryer was determined using image analysis.

The automated image analysis technique used contrast enhancement, filtering and thresholding to

enhance image quality and allow multiple images to be processed in order to quantify the amount

89

of solid within the flights of a rotating drum. Processed images were used to determine the

design load via different approaches and were reasonably similar. The approach based on the

saturation of the airborne solids and of the flight-borne solids in the upper half of the drum

demonstrated similar profiles and new phenomena. The peaks in the areas of the airborne solids

and of the flight-borne solids in the upper half of the drum may be used as a criterion to estimate

the design load but require highly accurate determination of area and also understanding flight-

borne solids bulk densities. The areas of first unloading flight (FUF) at different loading

conditions were fitted using a piecewise regression analysis and it is argued that they offer a

more suitable means to estimate the design load. The effects of rpm (2.5rpm, 3.5rpm, and 4.5

rpm) and solids cohesion on the design load were determined and found to be significant.

Additionally, airborne solids demonstrated increasingly dense and increasingly discontinuous

curtains as the degree of solids cohesion increased from a flow index (ffc) of 11 to 2.2.

A new methodology was developed to integrate image analysis and Eulerian-Eulerian CFD

simulation of free-falling curtains to estimate the mass of airborne solids at the design load. CFD

simulations of free-falling, non-cohesive curtains were well matched to the observed curtain

images. A consistent increase in the mass of airborne solids with increasing drum rotational

speed was observed. Image pixel intensities could be correlated to predicted CFD curtain solids

volume fractions at low solids volume fraction but became saturated at high volume fractions,

limiting the potential to use image analysis alone to determine curtain voidage. The

experimentally determined design loads were compared to common geometry-based design load

models available in literature and a modified equation based on the Baker (1988) model was

recommended. The ratio of airborne to flight-borne solids at the design load determined via

geometric analysis were similar and highly correlated to the ratios determined experimentally.

90

CHAPTER FIVE

5. SOLID TRA SPORT MODELLI G

This chapter outlines the development of a pseudo-physical compartment model for the MMG

industrial dryer. The MMG rotary dryer contains both unflighted and flighted sections. To the

best knowledge of the author, there is no literature describing these mixed mode dryers or their

modelling. However, there is extensive description of modelling both unflighted and flighted

drums in isolation. In this study, the modelling strategy for the flighted sections was based on a

compartment modelling approach. This modelling approach is a series-parallel formulation of

well-mixed tanks whereby the solid distributions between the compartments are estimated via

geometric modelling and design loading. The kilning phase occurring in the unflighted sections

was modelled using the axially-dispersed plug flow equation. RTD undertaken at different dryer

operating conditions (see Section 3.5) were used for model parameter estimation. The operating

conditions for all RTD trials presented in Tables 3.6, 3.8–3.11 are used as model inputs. The

geometrical configuration of the MMG industrial dryer presented in Section 3.2 is used to

describe the dryer in the geometric model. Simulations and parameter fitting were undertaken

using gPROMS (process modelling software). To verify the model structure and parameters, the

effect of operating conditions on RTD is investigated.

5.1 Model development

The model structure is presented in Figure 5.1. Following typical criterion (Matchett & Baker,

1988; Sheehan et al., 2005; Britton et al., 2006), airborne solids are regarded as active solids and

flight and drum borne solids are regarded as passive solids. Distinguishing between these two

solids phases is critical to the development of energy balances on these dryers. Studies have

modelled the solid transport in the flighted rotary dryer using different approaches: empirical

91

correlations, semi-empirical correlations, mechanistic, and compartment modelling. All these

approaches except compartment modelling do not account for the effect of flight configuration,

solid distribution, drum loading capacity and solid properties such as dynamic angle of repose.

The compartment model parameters are determined through geometric modelling based on dryer

geometry and solids physical properties. In this study, modelling of the flighted sections was

based on the pseudo-physical compartment modelling approach (Sheehan et al., 2005). The

original structure described in Sheehan et al. (2005) and Britton et al. (2006) accounted for

counter-current gas flow and flights that were of constant geometry and frequency down the

entire length of the dryer. The dryer examined in this study is a co-current dryer in which hot gas

flows in the same direction as the solids. Furthermore, different flight configurations are used

along the dryer length including the non-flighted sections.

Previous studies have assumed the solid transport within the unflighted dryer as plug flow with

(Danckwerts, 1953; Fan & Ahn, 1961; Mu & Perlmutter, 1980; Sai et al., 1990) or without (Ortiz

et al., 2003; Oritz et al., 2005) axial mixing. However, experimental studies have established the

occurrence of axial mixing phenomenon within the unflighted sections (Sai et al., 1990;

Bensmann et al., 2010). In this study, the unflighted sections were modelled as an axial dispersed

plug flow system.

92


5.1.1 Flighted section

The flow from the passive phase into the active phase in a given cell is characterised by transport

coefficient k2. The kilning flow is the movement of solids from passive cell to passive cell and is

characterised by transport coefficient k4. Previous studies have estimated the kilning flow

transport coefficient (k4) which was a function of kilning bed angle and rotational speed

(Sheehan et al., 2005; Britton et al., 2006). However, their approach did not utilize an obvious

physical representation of the kilning phase because the kilning or passive phase was modelled

as a well-mixed tank. A more physically realistic structure would be to use a dispersed plug

model or series of partial differential equations rather than ordinary differential equations.

Unfortunately, it is significantly more computational demanding to solve a system of partial

differential equations (plug flow model), particularly when coupled to the active phase which is

modelled using compartment modelling approach. A study by Lee et al. (2005) observed no

difference in the solutions obtained using either plug flow model or well-mixed tanks for the

Airborne solids

Passive to Active Kilning flows Active to Passive

Section E Section D Section B Section C Section A

Flight-borne and drum solids

93

active phase. In this study, the kilning flow was modelled using what is considered to be a more

physical realistic approach: dispersed plug flow model for the unflighted section.

The flow of solid from the active phase (k3ma) is divided into two different paths: axial

movement of falling solid into the next passive cell and the return of falling solid into the

corresponding passive cell. The splitting of the flow is governed by the forward step coefficient

(CF). Another important difference in the model structure between this study and that of Britton

et al. (2006) is the back-mixing flow caused by the airflow drag on the solids particles into the

active phase. In this study, there is no back-mixing flow into the active phase. The drag force

analysis showed there was minimal airflow drag effect on the solid particles and this can be

attributed to the physical properties of the solids. The mean particle size in this current study

varied from 18 mm to 6 mm while the mean particle size in Britton et al. (2006) was 0.84 mm.

Based on the model structure presented in Figure 5.2, the mass balances on solids for the two

phases and the tracer are described in Equations 5.1–5.3.

Figure 5.2: Model structure for the flighted section

k4i-1 k4i

k2i (1-CF) k3i

mai

mpi

CF k3i-1

CF k3i

94

The mass balance on solids in the passive cell i:

�5�"�? = 2�"��5�"�� + 2�"��\5("�� + 2�"�1 − �\�5(" − 2�"5�" − 2�"5�" 5.1

The mass balance on solids in the active cell i:

�5("�? = 2�"5�" − 2�"�\5(" − 2�"�1 − �\�5(" 5.2

The mass balance on tracer in the passive cell i:

�?�"5�"�? = 2�"��?�"��5�"�� + 2�"��\?("��5("�� + 2�"?("�1 − �\�5("− 2�"?�"5�" − 2�"?�"5�" 5.3

where mpi, mai, tai and tpi are passive mass (kg), active mass (kg), tracer concentration in active

phase (ppm) and tracer concentration in passive phase (ppm) respectively

5.1.2 Unflighted section

Figure 5.3: Model structure of the unflighted section characterised by its feed rate (Fs) and

length

Considering an unflighted section of the dryer as the system in Figure 5.3, the mass balance

equation across a differentiable element (∆z) along the length of the drum is:

hh? �T��∆K� = ¡�|£ − ¡�|£¤∆£ 5.4

∆z

Fs + dFs Fs

95

Mass flow rate (Fs) for the axially dispersed plug flow (Davis & Davis, 2003) is defined as:

� = @��T� − ℘��T�∆K 5.5

where us, ms, As and ρs are the solid velocity (m/s), kilning mass per length (kg/m), cross-

sectional area occupied by the solid (m2) and solid consolidated density (kg/m3) respectively.

By substitution,

hh? �T��∆K� = ¡`@��T� − ℘��T�∆K c¥£ − ¡`@��T� − ℘��T�∆K c¥£¤∆£ 5.6

Dividing by ∆z and taking the limit ∆z→ 0, and assuming ℘ is constant with respect to length

hh? ��T�� = ℘ h�hK� ��T�� − hhK �@��T�� 5.7

The term ��T� is the mass of solids per unit length and is an important property of the model as

it represents drum holdup

5� = ��T� 5.8

By substitution, the axially dispersed plug flow model for the unflighted drum is given as:

hh? �5�� = ℘ h�hK� �5�� − hhK �@�5�� 5.9

In similar manner, the mass balance for the tracer is:

hh? �j&5�� = ℘ h�hK� �j&5�� − hhK �j&@�5�� 5.10

where, j& is the tracer concentration(kg/kg).

5.1.3 Boundary conditions

The Danckwerts boundary conditions (Danckwerts, 1953) for Equations 5.9 and 5.10 were used

and are shown in Equations 5.11–5.14.

96

For Equation 5.9

K = 0, 5��0� = � @�� 5.11

At the outlet, the solids do not disperse back into the dryer and thus, the outlet boundary

condition is stated as follows:

K = m, ℘ h�5�hK� = 0 5.12

For Equation 5.10

K = 0, j&�0� = j"# 5.13

K = m, ℘ h�5�hK� = 0 5.14

5.2 Model parameters

Important model parameters include active cycle time �?�(�, passive cycle time �?��, and mass

average forward step (Davg). The active cycle time is the mass averaged falling time of the solid

(Figure 5.4). The passive time can be defined as the time it takes the discharge particle to travel

within the drum from the point it enters the passive phase to the original discharge position

(Figure 5.4). The average forward step is the axial distance the particle travels from the flight tip

to the dryer base, which is due to the inclination of the drum and the effect of airflow drag on the

particle (Figure 5.5). The average forward step (Davg) provides bounds on the maximum number

of cells since solids are constrained not to fall (geometrically) further than one cell ahead. In this

study, a drag force analysis on the particles indicated that drag can be neglected because of large

particle sizes of the zinc concentrate across the length of dryer. These model parameters

97

�?�(, ?��, �( 3� were determined via geometric modelling based on the mass contained within the

flights.

Figure 5.4: Drum cross section showing geometrical details (Active cycle time is the time

taken for the solids to fall from point ii to point i while passive cycle time is the time taken for the

discharge particle at point i to move to original discharged point ii).

Figure 5.5: Axial displacement of particle

ta

90o 270o

tp

ii

i

i

98

5.2.1 Geometric modelling

The cross-sectional area of solids within the flights and solids discharge rate from the flight are

calculated using geometric modelling described in Lee and Sheehan (2010). Lee and Sheehan

(2010) developed a geometric model based on the geometric characterisation of two-staged flight

using the number of flights, flight configuration, dryer geometry and mean surface angle. In their

study, the following model assumptions were made: the mean surface angle remains constant and

describes the behaviour of the solid across the entire rotation of the flight, the solids are free-

flowing and there is a continuous unloading process. Their experimental results showed that the

mean surface angle was not constant because of the avalanche discharge pattern of the solids

from the flights. However, their experimental flight unloading profile was within 95%

confidence interval of the predicted data, which indicated that the model assumptions are suitable

for this current study.

The geometric model (Microsoft Excel platform) which was developed by Lee (2008) was used

in this study. The key elements of the geometric model are the calculation of flight areas as a

function of rotation angle and the corresponding cycle times determined using Newton’s

equations of motion. Flight areas are differentiated with respect to time to obtain mass flow

rates. Mass averaged properties�Ψ� are determined within the geometric model using the

Equation 5.15 (Britton et al., 2006). The mass averaged properties determined in the geometric

model are mass averaged falling height, mass averaged falling time, mass average passive cycle

time.

Ψ = ∑ 5CC ?(∑ 5CC 5.15

99

The geometric model was modified to include the new design load model discussed in section

4.6. The modified equation based on Baker’s (1988) model is presented again in Equation 5.16.

The accurate estimation of the design load and loading state of the dryer directly influences

determination of the aforementioned model parameters.

��w�� yxv��(��" 6 = 1.24 × ¨d2 × e 5"#; f − 5\]\© 5.16

The interaction between the geometric model and the process model is shown in Figure 5.6. The

process model data (passive mass (mp) and moisture content (xw)) were exported into the

geometric model so as to calculate the model parameters�?�(, ?�� and the geometric constraints

of ª�( 3 , 5�«¬*®+¯. In order to simplify the initial fitting process, energetic processes were

excluded and a moisture content profile was assumed. The fitted equations for moisture content

and consolidated bulk density (Equations 3.1 and 3.4) as function of length along the drum were

used. In order to reflect the inlet and outlet moisture content for each RTD test, Equation 3.1 was

scaled for different RTD trials. The fitted linear equation of dynamic angle of repose versus

moisture content (Equation 3.2) was used to obtain the dynamic angle of repose for each model

compartment.

100

Figure 5.6: Geometric model structure

Regression models for the active and passive cycle times, mass averaged falling height and

design load were derived using the geometric model across a range of dynamic angle of repose

and loading state. These equations were used in gProms and are presented in Appendix F (sub-

section: geometric modelling for sections B, C and D). The regression model for the active and

passive cycle times were a function of the dynamic angle of repose, the loading condition of the

drum and the angle of inclination of the drum (Sheehan et al, 2005; Britton et al., 2006).

5.2.2 Flighted section

The transport coefficients 2� and 2� were calculated as the inverse of the passive and active

cycle times respectively (see Equation 5.17) (Sheehan et al., 2005; Britton et al., 2006). If the

Process model (gProms)

Mass and energy balance equations

mp, xw ?�(, ?��

�( 3 , 5�«¬*®+

Geometry model (Excel)

� Flight and drum geometrical configuration

� Dynamic angle of repose versus moisture content

� Rotational speed

� Loading state consideration

� Consolidated bulk density

101

mass in flight and drum solids exceeds the design load condition, the flow from the flight and

drum borne phase to airborne phase is set to maximum (Equation 5.18).

2� = 1?�� , 2� = 1?�( 5.17

5� > 5�)6�"3# , �2�5��±²³ = 2�5�«¬*®+ 5� ≤ 5�)6�"3# , 2�5� = 2�5�

5.18

Equation 5.19 shows the relationship between the kilning flow transport coefficient, solid

velocity and length of the compartment cell.

2��"� = @��"�m�"� 5.19

where 2��"�, @��"�, m�"� are kilning flow transport coefficient (s-1), solid velocity (m/s), and length

of the compartment cell (m) respectively.

The splitting of the flow from the active cell is governed by the forward step (CF), which was

calculated as the ratio of the average forward step (Davg) to the representative physical length of

the cell (Sheehan et al., 2005). The physical length of each compartment cell was calculated

geometrically based on the solids not falling further than one cell ahead, which constrained the

numbers of compartment cells within the flighted sections and is a key component in forcing

physical realism upon the system. The effect of compartment numbers is well described in Lee

(2010), as such reference to that analysis is provided. Thus, Equation 5.20 was used to determine

102

the number of cells within each flighted section. Table 5.1 gives the number of cells in the each

flighted section.

:� = m��( 3 5.20

where ?c, Ls and Davg are number of cells within the section, length of the section (m) and

average forward step (m) respectively.

Table 5.1: umber of cells in each flighted section

Section umber of cells (,c)

B 8

C 12

D 22

5.2.3 Unflighted section

The solid velocity and axial dispersion coefficients were assumed to be constant throughout the

dryer. Their estimation will be discussed in the parameter estimation section (Section 5.3.1).

5.2.4 Scaling effects

An internal examination of the dryer prior to the RTD experiment (Test 3) revealed significant

scale accumulation within the flights and the internal walls of the drum. Consequently, the study

assumed that the flight loading capacity was reduced by 80%. Figures 5.7 and 5.8 illustrate the

changes in the dryer geometry and flight configuration due the scale accumulation. A scale

accumulation factor (SF) was introduced in order to modify the geometrical configuration of the

flights and the drum. All the modified dimensions due to the scale build-up were used in the

103

geometric modelling. Equation 5.21 provides information on the calculation of the scale

accumulation factor.

Figure 5.7: Internal radius of a scale accumulated dryer

Figure 5.8: Scale accumulation around the flight base (s1) and the flight tip (s2)

The scale accumulation factor (SF) was calculated as follows:

R1

RD

SF

104

\ = w� × �F\

5.21

where w� and �F\ are flight base and percentage of area covered by scale accumulation

respectively. The percentage ranges between 0–100%.

5.3 Multi-scale model architecture

In this study, gPROMS (general process modelling system) numerical modelling software was

used in simulating the developed process models. The software has capability to solve systems of

integral, partial, ordinary and algebraic equations. There are different entities in the software:

model, process, estimation and experiment. The process entity provides the operating conditions

of the process, which includes the initial conditions, control variables and solution parameters.

The estimation and experiment entities are used for the parameter estimation and process

optimisation. The provision to build a model and sub-models is available in gPROMS, which is

suitable for multiscale modelling. The model and sub-models are linked via the defined data

streams. A detailed description of the components, programming approach and solvers in

gPROMS can be found in gPROMS (2004).

The numerical solver in gPROMS lacks the capacity to execute iterative model simulation. For

instance, an “IF or FOR loop” available in other programming languages is difficult to

implement in gPROMS. However, the advantage of gPROMS software is the interface with

other softwares such as FLUENT (Computational Fluid Dynamics software package), Microsoft

Excel and programming languages like FORTAN and C++. Due to the iterative nature of the

geometric model, Microsoft Excel was used. The linking of gPROMS to Microsoft Excel was

not undertaken because it is more computationally demanding. As a result, the regression models

for geometric modelling were developed in Microsoft Excel. gPROMS code for this study can be

105

found in Appendix F. Figure 5.9 shows the interaction between the geometry model and process

models.

Figure 5.9: Interaction between the process model and geometric model

5.3.1 umerical solution and parameter estimation

The solid velocity and the axial-dispersion co-efficient (℘) were the parameters estimated. The

parameter estimation process was executed in gPROMS software and was based on minimising

the sum of square errors between the modelled RTD and experimental RTD data points. The

following objective function (Equation 5.22) was used. There are different variance models in

gPROMS software and an appropriate variance model is chosen based on the magnitude of

standard deviation within the predicted or experimental data. In this study, the constant relative

variance model was used because the standard deviation values of the RTD data varied with the

magnitude of the tracer concentration. An initial guess value, and lower and upper limits of the

Airborne solids

Flight and drum

borne solids

Geometry model

Process model (gPROMS)

106

standard deviation are required. In this study, the initial guess value was 0.5, lower and upper

limits were 0.01 and 10 respectively.

Γ = K2 4��2�� + 12 min¸ ¹e e �4��U"C� � + �º>"C − º"C��U"C� �»¼

C��½*

"�� ¾ 5.22

where Z is the total number of measurements taken during the experiments, ϑ, α and βi, are the

set of model parameters to be estimated (us,℘), the number of experiments, and the number of

variables measured in ith experiment: 1 and the number of measurements of jth variable in the ith

experiment. ijY is the kth measured value of variable j in experiment i. Yij is the jth predicted

value of variable j in experiment i. 2

ijσ is the variance of the jth measurement of variable j in

experiment i. 2

ijσ is described by the models available in gPROMS.

Preliminary runs found that discretisation scheme and number of discretised cells within the plug

flow models have significant effect on the accurate estimation of the parameters and the fitting of

the RTD profile. Figure 5.10 shows the effect of grid spacing within the unflighted sections on

the fitting of the RTD profile. Large grid sizes (0.3 m and 0.15 m) resulted in numerical

instability. The grid independency study revealed that the fitted RTD profiles of 0.075 m grid

size and 0.0375 m grid size were similar. Based on 0.075 m grid size, the number of discretised

cells for sections A and E were 28 and 100 respectively. It should be noted that the two

unflighted sections (sections A and E) were discretised using second order backward finite

difference scheme.

107

Figure 5.10: Effect of grid size within the unflighted section

Table 5.2 presents the estimated model parameters for different RTD trials. Lee (2008) reported

estimated kilning velocity of 0.04 m/s for a counter-current industrial sugar dryer. The value is

approximately of the same order of magnitude as that of this study (0.01–0.03 m/s). The low

solid velocity suggested that the kilning flow is a dominant flow path in the model structure

because there were more solids in the passive phase.

Sherritt et al. (2003) performed a non-invasive technique to measure the axial mixing in a

rotating drum and the axial dispersion coefficients were calculated. The estimated axial

dispersion coefficient values in this current study (Table 5.2) were within their proposed range of

10�� to 10�� m2/s. Sherritt et al. (2003) also concluded that the axial dispersion coefficient is

proportional to the diameter of the drum and to the square root of the rotational speed. This

relationship could not be verified due to limited experimental data.

-20

-10

0

10

20

30

40

50

60

500 700 900 1100 1300 1500Tra

cer

con

cen

tra

tio

n (

pp

m)

Time (seconds)

0.3 m grid size

0.15 m grid size

0.075 m grid size

0.0375 m grid size

Experimental data

108

Table 5.2: Estimated parameters for different conditions in the dryer

Trials us (m/s) ℘℘℘℘ (m2/s)

Test 2 0.020 0.0023

Test 3 0.030 0.00024

Test 4 0.016 0.00040

Test 5 0.011 0.00044

Test 6 0.015 0.00090

In order to understand the effect of operating conditions on the estimated parameters, the

relationships between the estimated parameters and operating conditions were examined using

the Pearson correlation technique (Mendenhall, 1979). The Pearson correlation technique is used

to determine the significance of interaction between the variables. The Pearson correlation

technique in Microsoft Excel was used to analyse the data presented in Table 5.2. The Pearson

linear correlation coefficients between the estimated parameters and operating conditions are

presented in Table 5.3.

Table 5.3: Pearson correlation coefficients between the axial dispersion coefficient and

experimental conditions

Parameters

Pearson correlation coefficient

Rotational speed

(rpm)

Internal diameter

of the drum (m)

Inlet dynamic angle

of repose (o)

@� 0.67 - 0.77 0.22

℘ 0.27 0.41 0.98

109

Results indicate there was a significant correlation between the axial dispersed coefficient and

the inlet dynamic angle of repose (r = 0.98). There was weak relationship between the internal

diameter of the drum and the axial dispersed coefficient. The correlation coefficients showed the

main operating conditions affecting the solid velocity are rotational speed (r = 0.67) and the

internal diameter of the drum (r = -0.77). However, a t-test at 95% confidence interval indicated

that they were not statistically significant and this can be attributed to the limited experimental

data. At a wider range of experimental conditions, there is a greater chance of demonstrating a

significant relationship.

To ensure the solids transport model for the unflighted sections is responsive to geometric and

operating variables, it is necessary to derive a suitable model for the solid velocity and dispersion

coefficient based on the abovementioned operating conditions. Solid velocity was modelled as a

function of the rotational speed and internal diameter of the drum. The axial dispersed coefficient

was modelled as function of inlet dynamic angle of repose. Estimated values for solid velocity

and axial dispersed coefficient are presented in Table 5.2 and the corresponding operating

conditions ��, Y, ∅ � were used in Microsoft Excel’s multiple regression analysis to develop

Equations 5.23 and 5.24 for estimating the solid velocity and axial dispersed coefficient

respectively. The regression models were implemented in the solid transport model to study the

effect of operating variables.

@� = 0.161318 + 0.006533 Y − 0.04198 � �� = 0.82� 5.23

℘ = 0.000197∅ − 0.01154 �� = 0.97� 5.24

110

5.4 Model results

The fitted data and experimental data for different conditions are plotted in Figures 5.11–5.15.

The model RTD profiles well matched the experimental RTD profiles for the different operating

conditions of the dryer, which indicated that the proposed model structure was appropriate for

the studied rotary dryer. The key features of initial steep rise and extended tail in the RTD

profiles were also reproduced by the model.

Figure 5.11: RTD profile (Test 2)

0

5

10

15

20

25

450 550 650 750 850 950 1050 1150

Tra

cer

con

cen

tra

tio

n (

pp

m)

Time (seconds)

Experimental RTD

Simulated RTD

111



0

5

10

15

20

25

500 600 700 800 900 1000 1100 1200

Tra

cer

con

cen

trati

on

(p

pm

)

Time (seconds)

Experimental RTD

Simulated RTD

0

10

20

30

40

50

60

650 750 850 950 1050 1150 1250 1350

Tra

cer

con

cen

tra

tio

n (

pp

m)

Time (seconds)

Experimental RTD

Simulated RTD

112



0

5

10

15

20

25

30

35

800 1000 1200 1400 1600 1800 2000

Tra

cer

con

cen

trati

on

(p

pm

)

Time (minutes)

Experimental RTD

Simulated RTD

0

5

10

15

20

25

30

35

600 700 800 900 1000 1100 1200 1300 1400

Tra

cer

con

cen

tra

tio

n (

pp

m)

Time (seconds)

Experimental RTD

113

Table 5.4 outlines the mean residence time and holdups for different conditions of the dryer. The

model predictions of the mean residence time and hold-ups were comparable to the experimental

values presented in Table 3.14. Design load considerations within the compartment model

facilitated better estimation of solids distribution within the dryer as shown Figure 5.16–5.21 for

Tests 2, 3, 4, 5 and 6 respectively. The study noticed that movement of solids was faster in the

flighted sections compared to the unflighted sections. As a result, the solid holdups within the

unflighted sections were large. On the other hand, the experimental solid outlet moisture content

for Test 3 was high (Table 3.8), which indicated there was minimal gas-solids interaction and is

confirmed by Figure 5.17. The reduction in its flight loading capacity also resulted in an

overloaded condition as there were excess solids rolling in the base of the dryer (Figure 5.17) .

Table 5.4: Holdup for different operating conditions of the dryer

Test

Mean residence

time (minutes)

Average feed rate

(kgwet solid/min)

Holdup

(kgwet solid)

Test 2 12.08 2840 34,300

Test 3 13.93 3140 43,700

Test 4 15.26 2440 37,200

Test 5 21.58 1940 41,900

Test 6 15.68 2690 42,000

114

Figure 5.16: Solids distribution within the flighted sections for Test 2 (Holdup in the

unflighted sections: 2237 kg/m)



0

50

100

150

200

250

300

350

400

0 2 4 6 8 10 12 14 16

Mass

(k

g)

Axial position (m)

Design load(Passive)

Passive mass

Active mass

0

100

200

300

400

500

600

0 5 10 15 20

Ma

ss (

kg

)

Axial position (m)


Passive mass

Active mass

115





0

50

100

150

200

250

300

350

0 2 4 6 8 10 12 14 16

Mass

(k

g)

Axial position (m)


Passive mass

Active mass

0

50

100

150

200

250

300

350

0 2 4 6 8 10 12 14 16

Ma

ss (

kg)

Axial position (m)


Passive mass

Active mass

116



5.4.1 Model sensitivity

In order to verify the model structure and the parameters, the effects of operating conditions on

the RTD profile and the solid distribution between the active and passive phases within the

model were examined.

5.4.1.1 Effect of internal diameter

The internal diameter of the dryer and the flight dimensions change as the solid adheres to the

walls and flights of the dryer. In order to investigate its effect on the dryer performance

indicators, the rate of solid accumulation on the walls was achieved by varying the scaling

percentage presented in Equation 5.21. The other operating conditions for the investigation are

presented in Table 3.8 (Test3) and remained constant. Figure 5.21 shows the effect of the

internal diameter on the RTD profiles. In this study, the effect of the internal diameter was

0

50

100

150

200

250

300

350

0 2 4 6 8 10 12 14 16

Ma

ss (

kg

)

Axial position (m)


Passive mass

Active mass

117

similar to the Friedman and Marshall (1949a) correlation that mean residence time is inversely

proportional to the internal diameter. Figures 5.22 and 5.23 illustrate the solid distribution within

the flighted section of the dryer. The active phase reduces significantly with an increase in the

hard scale build-up in the drum.

Figure 5.21: Effect of internal diameter and flight loading capacity on RTD

0

5

10

15

20

25

30

600 700 800 900 1000 1100 1200

Tra

cer

con

cen

tra

tio

n (

pp

m)

Time (seconds)

20% scaling

40% scaling

60% scaling

80% scaling

118

Figure 5.22: Effect of internal diameter on solid distribution (passive)

Figure 5.23: Effect of internal diameter on solid distribution (active)

280

330

380

430

480

530

580

0 2 4 6 8 10 12 14 16

Fli

gh

t an

d d

rum

bo

rne

soli

ds

(kg)

Axial position (m)

20 % scaling

40 % scaling

60 % scaling

80 % scaling

0

10

20

30

40

50

60

0 5 10 15 20

Air

bo

rne

soli

ds

(kg

)

Axial position (m)

20 % scaling 40 % scaling

60 % scaling 80 % scaling

119

5.4.1.2 Effect of rotational speed

The effect of rotational speed on the RTD and solid distribution between the compartments was

investigated. The rotational speed was varied between 2 rpm and 5 rpm while the other operating

conditions presented in Table 3.9 remained constant. Figure 5.24 shows the effect of the

rotational speed on RTD. The mean residence time decreases with an increase in the rotational

speed. This trend was observed in Hatzilyberis and Androutsopoulos’s (1999) experimental RTD

study for the flow of lignite particles through a rotary dryer. Figures 5.25 and 5.26 describe the

effect of rotational speed on the solid distribution in the flighted sections of the dryer. As the

rotational speed increases, the active cycle time reduces, which means solids spend less time

within the airborne phase (Figure 5.26). However, the ratio of airborne solids to flight-borne

solids increases with an increase in the rotational speed. The study has further established the

ability of the pseudo-physical compartment model as a design and control tool for industrial

applications. Therefore, it is necessary to develop and incorporate energy balances into the

validated solid transport model in order for it to be used as a design and control tool in the

industry.

120

Figure 5.24: Effect of rotational speed on RTD

Figure 5.25: Effect of rotational speed on solid distribution (passive)

0

10

20

30

40

50

60

70

80

400 600 800 1000 1200 1400 1600 1800 2000

Tra

cer

con

cen

tra

tio

n (

pp

m)

Time (seconds)

2 rpm 2.5 rpm

3 rpm 3.5 rpm

4 rpm

140

190

240

290

340

390

440

0 2 4 6 8 10 12 14 16

Fli

gh

t a

nd

dru

m b

orn

e so

lid

s (k

g)

Axial position (m)

2 rpm 2.5 rpm

3 rpm 3.5 rpm

4 rpm

121

Figure 5.26: Effect of rotational speed on solid distribution (active)

5.5 Summary

The modelling of solid transport within an industrial rotary dryer was undertaken. The unflighted

sections of the dryer were modelled as axial dispersed plug flow systems and compartment

modelling approach was used to model the flighted sections. A parameter estimation technique

based on the constant relative variance model was used to determine the solid velocity and the

axial dispersion coefficient. A test of Pearson correlation showed the relationship between the

estimated parameters and the operating conditions. The study also investigated the effect of solid

adhesion to the walls of the dryer and found the active mass decreases sharply as the scale

accumulation within the drum increases. The model’s response to operating variables

demonstrated its capability as a design and control tool.

30

34

38

42

46

50

0 5 10 15 20

Air

born

e s

oli

ds

(kg)

Axial position (m)

2 rpm 2.5 rpm

3 rpm 3.5 rpm

4 rpm

122

CHAPTER SIX

6. MATHEMATICAL MODELLI G OF A I DUSTRIAL FLIGHTED ROTARY

DRYER

This chapter focuses on the development and integration of energy balances into the validated

solid transport model (Chapter 5). In order to facilitate the drying process, a gas phase model is

introduced. The gas phase in both unflighted and flighted sections was modelled as a plug flow

system. Simulations and parameter estimation were undertaken using gPROMS (process

modelling software). Parameter estimation and model validation was carried out using the

experimental moisture content and RTD data. The model was used to predict the gas and solid

internal temperature profiles.

6.1 Model development

6.1.1 Model structure

The solid transport model structure developed in Chapter 5 is extended to include the gas phase

(Figure 6.1). Heat and evaporated water were transferred between these phases. Heat was

transferred to the solid from the gas by convection (Qconv) and radiation (Qrad). The study

assumed that most of the drying process occurred in the active phase of the flighted sections

while minimal drying occurred in the unflighted sections. There is uncertainty in the modelling

and dynamics of the gas phase. The mean residence time of the gas phase was around 5 seconds

compared to the solid phase of 15 minutes. As a result, the gas phase in both the flighted and

unflighted sections was assumed to be a plug flow system without dispersion. The study assumed

heat is lost through the shell from the gas phase and the contact between the shell and solids was

ignored in the heat loss calculation.

123


6.1.1.1 Reference states

The reference state for water was liquid at 0 °C and 1 atm. The reference states for the solid and

gas were 0 °C and 101.325 kPa.

6.1.1.2 Flighted section

6.1.1.2.1 Solid phase

Figure 6.2 represents the model structure for the flighted section. Equations 5.1 and 5.2 are the

dry solid mass balance in passive and active phases respectively. To facilitate energy balance, it

Heat loss (Qloss) (J/s)


Section E Section D Section B Section C Section A

Convective heat transfer (Qconv) (J/s)

Evaporation rate (Rw) (kg/s)

Radiation heat transfer (Qrad) (J/s)

124

is necessary to augment the dry solids mass balance with a solids moisture balance. Equations

6.1 and 6.2 describe the solid moisture balance for the passive and active phases.

Figure 6.2: Model structure of the flighted section

The moisture balance on solids in the passive cell i:

��j"5�"��? = jI"��5�"��2�"�� + jI"��5("��2�"��\+ jI"5("2�"�1 − �\� − jI"5�"2�" − jI"5"2�"

6.1

k2i (1-CF) k3i

k4i-1 k4i

mai

mpi

CF k3i-1

CF k3i

mgi

Heat loss (Qloss) (J/s)

Convective heat transfer (Qconv) (J/s)

Evaporation rate (Rw) (kg/s)

Radiation heat transfer (Qrad) (J/s)


125

The moisture balance on solids in the active cell i

�jI"5("�? = jI"5�"2�" − jI"5("2�"�\ − jI"5("2�"�1 − �\� − �I�"� 6.2

Energy balance on solids in the passive cell i (assuming incompressible solid phase):

� ª5�"jI"��I~��" + 5�"�1 − jI"��~��"¯�?= ªjI"��I~��"�� + �1 − jI"��~��"��¯ . 2�"5�"��+ �jI"��I~�("�� + �1 − jI"��~�("��. 2�"��\5("��+ �jI"��I~�(" + �1 − jI"��~�("�. 2�"�1 − �\�5("− ªjI"��I~��" + �1 − jI"��~��"¯ . 2�"5�"− ªjI"��I~��" + �1 − jI"��~��"¯ . 2�"5�"

6.3

Energy balance on solids in the active cell i (assuming incompressible solid phase):

��jI"5("��I~�(" + �1 − jI"�5("��~�("��?

= ªjI"��I~��" + �1 − jI"��~��"¯ . 2�"5�"− �jI"��I~�(" + �1 − jI"��~�("�. 2�"�\5("− �jI"��I~�(" + �1 − jI"��~�("�. 2�"�1 − �\�5("− �I�"�� + ��I~�("� + ¿�$# �"� + ¿'()�"�

6.4

In Equations 6.1–6.4, ma, mp, xw ,Cps, Cpw, Hv, Ts and Rw, are active mass (kg), passive mass (kg),

moisture content (kg/kgwet solid), specific heat capacity of zinc concentrate (J/(kg.K)), specific heat

capacity of liquid water (J/(kg.K)), latent heat of vaporization (KJ/kg) at temperatature = 0 oC,

126

solid temperature (oC) and evaporation rate (kg/s) respectively. The specific heat capacities for

liquid water and solid were assumed to be constant across the anticipated temperature range (25

to 55 oC).

6.1.1.2.2 Gas phase

The gas dynamics in terms of residence time is significantly different to the solid phase. The gas

velocity across the dryer was between 3–5 m/s compared to the solid phase of 0.0155 m/s. As a

result, the gas phase within the flighted section was modelled algebraically as a plug flow

system, i.e. a steady state system (Duchesne et al., 1997). The equations for the mass balances

and enthalpy balance are stated in Equations 6.5–6.7.

The mass balance equation of the gas is:

3*ÀÁ = 3* + �I�"� 6.5

The equation for the moisture balance in the gas is:

3*ÀÁGI*ÀÁ = 3*GI* + �I�"� 6.6

Taking the following energy pathways into consideration, the water was heated to 100 oC, energy

was required to evaporate the water and later heated to the operating temperature. The equation

for the enthalpy balance in the gas is:

127

3*ÀÁ�1 − GI*ÀÁ��3~I3*ÀÁ + 3*ÀÁGI*ÀÁ��I~I3*ÀÁ + 3*ÀÁGI*ÀÁ� + 3*ÀÁ�1 − GI*ÀÁ��3�~3"¤� − 100�+ 3*ÀÁGI*ÀÁ�� ~3"¤� − 100� = 3*�1 − GI*��3~I3* + 3*GI*��I~I3* + 3*GI*� + 3*�1 − GI*��3�~3" − 100� + 3*GI*�� ~3" − 100�+ �I�"�� + ��I~�Â*� − ¿�$# �"� − ¿'()�"� − ¿Q$��"�

6.7

where Fg, Cpg, Cpw, Cpv Twg , Tg and Qloss are gas flow rate (kg/s), specific heat capacity of gas,

specific heat capacity of liquid water((J/(kg.K)), specific heat capacity of water vapour

((J/(kg.K)), gas temperature (0–100 oC), operating gas temperature and heat lost through the shell

respectively.

6.1.1.3 Unflighted section

Figure 6.3 shows the model structure in the unflighted sections. The solid phase in the unflighted

sections was modelled as an axially-dispersed plug flow (Section 5.1.2). The gas phase in this

section was also assumed to be a plug flow system without dispersion.

128

Figure 6.3: Model structure of the unflighted section

6.1.1.3.1 Solid phase

To facilitate energy balance and drying, it is necessary to augment the dry solids mass balance

(Equation 5.9) with the solids moisture balance. Following the approach taken in Section 5.1.2,

the mass balance on moisture content in the solid phase is:

hh? �jI5�� = ℘ h�hK� �jI5�� − hhK �@�jI5�� − �I∆K 6.8

where ms and Rw are the mass per length (kg/m)and the rate of moisture removal (kg/s) within a

slice (∆z) respectively.

Energy balance in the solid phase including convection (Qconv), radiation (Qrad) and evaporation

is expressed as:

Solid phase

Gas phase Fg + dFg Fg (kg/s)

Fs + dFs Fs (kg/s)

∆z (m)

Convective heat transfer (Qconv) (J/s) Radiation heat transfer (Qrad) (J/s)

Evaporation rate (Rw) (kg/s) Heat loss (Qloss) (J/s)

129

hh? �T�A��∆K� = ¡��|£ − ¡��|£¤∆£ − �I�� + ��I~�� + ¿�$# + ¿'() 6.9

where A�, �� are the internal energy (J/kg) and enthalpy energy (J/kg) respectively.

As a result of the assumed incompressibility of the solids (i.e. <=>>>> ≅ 0), internal energy A�� was

simplified to:

hA�� = h�� = ��h~� 6.10

Substituting for Fs (Equation 5.5) and �� in Equation 6.9 and dividing by ∆z and taking the limit

∆z→ 0, Equation 6.9 becomes:

hh? �jI5��I~� + �1 − jI�5��~��= ℘ h�hK� �jI5��I~� + �1 − jI�5��~��− @� hhK �jI5��I~� + �1 − jI�5��~��− �I∆K �� + ��I~�� + ¿�$# ∆K + ¿'()∆K

6.11

6.1.1.3.2 Gas phase

Assuming plug flow without dispersion, the mass balances on dry gas and moisture can be

derived (Equations 6.12–6.14). As the hot gas flows through the dryer, heat is transferred to the

solids and the moisture content of the gas increases due to the evaporated water. This leads to

variation in the gas density along the length of the dryer such that T3 = ��K�.

The mass balance equation on the gas across a differential element (∆z) is

130

hh? �T3�3∆K� = ¡�3�3T3�£ − ¡�3�3T3�£¤∆£ 6.12

Substituting the term �3T3 = 53 into Equation 6.12, then dividing by ∆z and taking the limit

∆z→ 0, gives

hh �53� = − hhK ��353� 6.13

The mass balance on moisture in the gas is:

hh? �GI53� = − hhK ��3GI53� + �I∆K 6.14

In Equations 6.12 –6.14, Ag, ρg, mg, yg and Rw are the area (m2), density (kg/m

3), mass per length

(kg/m), gas humidity (kg/kg Total wet gas) and drying rate (kg/s) respectively. The gas velocity is

calculated as follows:

�3 = 3T3�3 6.15

Energy balance on the gas across a differential element (∆z) is:

hh? �T3A3�3∆K�= ¡�3�3T3��£ − ¡�3�3T3��£¤∆£ + �I�� + ��I~�� − ¿�$# − ¿'() − ¿Q$��

6.16

Noting the compressible nature of the gas phase, the following substitution, assuming ideal gas

behaviour is made:

A�3 = ��3 − <=>>>>3 = ��3 − �~>>>>3 6.17

Dividing by ∆z and taking the limit ∆z→ 0 and substituting the ideal gas equation for <=>>>>>, gives:

131

h�GI�3T3��I~3 + �1 − GI��3T3��3~3 + GI�3T3� − ��~�3 − ��~�I�h?= − h��3GI�3T3 ��I~3 + �3�1 − GI��3T3��3~3 + �3GI�3T3� �hK+ �I∆K �� + ��I~�� − ¿�$# ∆K − ¿'()∆K − ¿Q$��∆K

6.18

Taking the following energy pathways into consideration, the water was heated to 100 oC, energy

was required to evaporate the water and later heated to the operating temperature (for instance,

500 oC). Equation 6.18 becomes:

h dGI53��I~I3 + �1 − GI�53��3~I3 + GI53� + GI53�� ~3 − 100� +�1 − GI��3�~3 − 100� − ��~�3 − ��~�I f

h?

= −h d�3GI53 ��3~I3 + �3�1 − GI�53��3~I3 + �3GI53� +

�3GI53�� ~3 − 100� + �3�1 − GI�53��3�~3 − 100� fhK

+ �I∆K �� + ��I~�� − ¿�$# ∆K − ¿'()∆K − ¿Q$��∆K

6.19

In Equation 6.19, R and n are the ideal gas constant (J/(mol·K)) and the number of moles (mol))

respectively.

6.1.1.3.3 Boundary conditions

The Danckwerts boundary conditions (Danckwerts, 1953) for Equations 5.9, 6.8, 6.11, 6.13, 6.14

and 6.19 were used and are shown below.

For Equation 5.9

132

K = 0, 5��0� = � @�� 6.20

At the outlet, the solids do not disperse back into the dryer and thus, the outlet boundary

condition is stated as follows:

K = m, ℘ h�5�hK� = 0 6.21

For Equation 6.8

K = 0, jI�0� = j"#Q6& 6.22

K = m, ℘ h�jI5�hK� = 0 6.23

For Equation 6.11

K = 0, ~��0� = ~��"#Q6&� 6.24

K = m, ℘ h��I~�jI5� + ��~��1 − jI�5��hK� = 0 6.25

For Equation 6.13

K = 0, 53�0� = 3 �3� 6.26

K = m, h53hK = 0 6.27

For Equation 6.14

K = 0, GI�0� = G"#Q6& 6.28

133

K = m, hGI53hK = 0 6.29

For Equation 6.19

K = 0, ~3�0� = ~3�"#Q6&� 6.30

K = m, h d�3GI53 ��I~I3 + �3�1 − GI�53��3~I3 + �3GI53� +

�3GI53�� ~3 − 100� + �3�1 − GI��3�~3 − 100� fhK = 0

6.31

6.1.1.4 Drying rate

The drying rate in the rotary dryer depends on the drying gas, the properties of the solid and the

geometrical configuration of the dryer. The drying rate is controlled by either the rate of internal

migration of water molecules to the surface or the rate of evaporation of water molecules from

the surface into the air. It can be characterised experimentally by measuring the moisture content

loss as a function of time. Studies have also used thin-layer drying experiments to study the rate

of evaporation and to derive drying rate correlations (Cao & Langrish, 2000; Igauz et al, 2003).

Wang et al. (1993) suggested the drying rate in the falling rate period can be determined by using

Sharples et al. correlation (1964). These approaches are not suitable for this study because the

thin layer experiments and the correlations were carried out at a lower temperature range

compared to the typical operating temperature of this study.

In a non-experimental approach, the drying rate has been typically modelled as the process of

water molecules transferring into the gas stream and the driving force was provided by the

difference in the vapour pressures of the gas and the wet surface (Duchesne et al. 1997;

Didriksen, 2002; Raffak et al. 2008). The rotary dryer examined in Duchesne et al. (1997) and

134

Raffak et al. (2008) were used in drying zinc concentrates and phosphate ore respectively. In this

study, the drying rate was assumed to be proportional to the difference between the water partial

pressure in the gas phase and the water vapour pressure at the temperature of the solids being

dried (Equation 6.32). The vapour pressure was calculated using the solid temperature of the

active phase and was estimated using Antoine equation (Equation 6.33)

�I = ℎ1��<I − < � 6.32

where hm, Pw, Pv and As are the mass transfer coefficient, water vapour pressure at the

temperature of the solids being dried, partial pressure of water vapour in the gas phase and

surface area of solid particles in contact with the incoming gas respectively. The estimation of

the surface area of solid particles for unflighted section and flighted section will be discussed in

subsequent section (where As = Aa or As = AAL).

Vapour pressure at the temperature of the airborne solids is expressed by Felder and Rousseau

(2005) as:

<I = exp `23.561 − 4030.182~� + 235 c 6.33

Pw and Ts are water vapour pressure (Pa) and temperature of the solids (oC)

Partial pressure of water vapour in the gas phase is calculated by:

< = GI< 6.34

GI , <Ç are the gas humidity (mol/mol) and total pressure (Pa) respectively.

135

6.1.1.5 Heat and mass transfer

During drying of wet solids in rotary dryers, heat and mass transfer occurs simultaneously. In

this thesis, the heat is assumed to be transferred from the gas to the solid particles through

radiation and convection.

6.1.1.5.1 Convective heat transfer

The convective heat transfer (Qconv) is dependent on the temperature difference between the

drying gas and the solid. The equation for convective heat transfer can be expressed in Equation

6.35:

¿�$# = ℎ��~� − ~3� 6.35

where Qconv, hc, As, Ts and Tg are the convective heat transfer, convective heat transfer coefficient,

surface area, temperature of the solid and temperature of the air respectively.

The process of estimating the convective heat transfer coefficient can be achieved through the

correlation of the heat transfer coefficient and the dimensionless Nusselt number (?u). The

general form of this type of correlation is as follows:

:@ = ℎ�m23 = ��, <, È@� 6.36

where ?u, , hc, L, kg, Re, Gu and Pr, are the Nusselt number, heat transfer coefficient,

characteristic length scale, thermal conductivity, Gukhman number, and Prandtl number

respectively.

The most commonly used Nusselt correlation in rotary dryer modelling studies is the Ranz and

Marshall (1952) correlation (Equation 6.37). The correlation was based on evaporation of water

136

droplets experiments and non-interaction between the droplets was assumed. This assumption is

not valid for solid particles within the rotary dryer.

:@ = 2 + 0.6��.�<�.�� 6.37

Hirosue (1989) introduced a correction factor into the Ranz-Marshall (1952) correlation to

address the limitation of non-interaction between the falling particles. The correction factors are

stated in Equations 6.38 and 6.39.

Range 1

ÉÊ = 37.5�� ⁄ , 3 × 10� ≤ �� ≤ 1.5 × 10Ë 6.38

Range 2

ÉÊ = 4190�� ⁄ , 1.5 × 10Ë ≤ �� ≤ 2 × 10�� 6.39

�� = ��.��.�� 6.40

In Equations 6.38–6.40, Kh, Fr, S, X and dp are the correction factor, Froude number, cross-

sectional area of the dryer, holdup and particle diameter respectively.

Previous studies in rotary dryer modelling (Kelly, 1987; Didriksen, 2002; Raffak et al., 2008)

have also used Nusselt number correlation (Equation 6.41) developed for air flow over spherical

particles. Equation 6.41 was used to determine the convective heat transfer coefficient in this

thesis.

137

:@ = 0.33��.� 6.41

6.1.1.5.2 Radiation heat transfer

The study assumed that the heat transferred from the gas to the solid by convection and radiation.

It should be noted that most of the drying process was assumed to occur in the active phase of

the flighted sections while minimal drying occurred in the unflighted sections. This is a typical

approach taken in flighted rotary dryer literature (Duchesne et al, 1997; Sheehan et al., 2005).

The exposure of both the active phase and the active layer of the unflighted sections to freeboard

gas promote gas-solids interactions within the dryer. The description and implications of the

choice of the active layer will be discussed in Section 6.1.1.7.1. Equation 6.42 presented in

previous studies (Didriksen, 2002; Dhanjal et al., 2004) was used to calculate the radiative heat

transfer from the gas to the solid. This equation represents the radiative exchange between the

freeboard gas and the active solids within an active phase cell, and also within the unflighted

sections. The radiative exchanges that are neglected in this work are the exchange between the

freeboard gas and passive solids as well as the exchange between the internal walls and the

solids. A more comprehensive approach described in rotary kiln and combustion chamber

literature (where gas temperatures are typically much higher) is the zone method. This has been

used to determine the radiative heat transfer within complex geometries (Gorog et al (1981),

Barr, 1986; Batu and Selcuk, 2002). This approach involves subdividing the enclosure into zones

and summing the exchanges of radiation between the neighbouring zones. The model developed

in this thesis would provide a good basis with which to implement such an approach because the

model is already geometrically segmented. However, the shortcomings of this approach are large

computing requirements and numerical instability due to large number of non-linear equations. It

should also be noted that the effect of radiative heat transfer in the current study is expected to be

138

relatively small because the gas temperature is lower than 700oC, where radiation is known to

dominate. The radiative heat transfer from the gas to inside wall of the dryer was also considered

and discussed in section 6.1.1.6. The end walls were neglected because their areas only account

for roughly 5% of the total exposed area.

¿'() = N'U'�~3� − ~�� 6.42

6.1.1.5.3 Mass transfer

The mass transfer coefficient (hm) can be calculated from the Ranz and Marshall (1952)

correlation stated in Equation 6.43, which was based on single particle approach.

ℎ = 2 + 0.6��.�<�.�� 6.43

where Sh is the Sherwood number (Equation 6.44)

ℎ = ℎ1m℘²Ì 6.44

In this study, the mass transfer coefficient was calculated via the Chilton-Colburn analogy (jH=

jm) used to relate mass and heat transfer coefficients, as previously used in other rotary dryer

modelling studies (Didriksen, 2002; Raffak et al., 2008)

/0 = ?<� �⁄ 6.45

/1 = �ℎ1< �3T3 � �� ⁄ 6.46

139

where jH, jm, Pv, vg, ρg, Sc and St are the heat transfer factor, mass transfer factor, vapour

pressure, gas velocity, gas density, Stanton number, Schmidt number and Prandtl number

respectively

Thus, the mass transfer coefficient (hm) is:

ℎ1 = ` ? �3T3< c `< �c� �⁄ 6.47

The Stanton (St) and Schmidt (Sc) numbers can be estimated using Equations 6.48 and 6.49

respectively.

? = ℎ��3 �3T3 6.48

� = S3℘²ÌT3 6.49

where hc, Cpair and ℘²Ì are heat transfer coefficient, specific heat capacity of the air and vapour

diffusivity in the air respectively.

6.1.1.6 Heat loss

The heat loss from the dryer shell was calculated by determining individual thermal resistances

and the overall temperature gradient, according to Equation 6.50 (Sheehan, 2002).

¿Q$�� = OQ$�� ~3 − ~(1u∑ �C � 6.50

where Tg, Tamb and Rj, are gas temperature, ambient temperature and resistance respectively. A

heat loss turning factor (θloss) is introduced in order to fit the gas outlet temperature, and its

estimation process is discussed in the parameter estimation section.

140

In this study, the contact between the solids and the walls that acts as an insulator was ignored in

the resistance analysis. Hence, the heat loss over the entire circumference of the shell was

assumed. The following mechanisms of heat transfer were considered in the resistance analysis:

forced convection from the hot gas to the dryer inside surface, free convection from the outside

dryer surface, radiation from the hot gas to the dryer inside surface, radiation from the outside of

the dryer surface and conduction.

e �C = 1�ℎ"#2�"#m + ℎ'()*+2��m� + ln��$ "#⁄ �2�2�"#m+ 1�ℎ$%&2��$m + ℎ'(),-.2��$m� 6.51

The total heat coefficient (convection�ℎ"#� and radiation �ℎ'()*+�� at the internal surface of the

dryer was determined. The Sieder and Tate (1936) correlation was used to calculate the forced

convective heat transfer coefficient (Equation 6.52) because the effect of variation in the gas

temperature and its properties across the dryer was taken into account. The radiation heat transfer

coefficient was estimated using Equation 6.53 (Incropera & DeWitt, 2002).

ℎ"# = � 23�"#� × �0.027�� ⁄ <� �⁄ ` SS�c�.�� 6.52

ℎ'()*+ = N'U'�~3 + ~I��~3� + ~I�� 6.53

The total heat coefficient (convection�ℎ$%&� and radiation �ℎ'(),-.� at the external surface of the

dryer was calculated using available correlations. The Churchill and Chu (1975) correlation was

141

used to calculate the convective heat transfer coefficient (Equation 6.54) and Equation 6.55 was

used to calculate the external radiation heat transfer coefficient (Incropera & DeWitt, 2002).

ℎ$%& = �23,-.�$%& � ×ÎÏÏÐ0.60 + 0.387�v� �⁄

�1 + ª0.559 <� ¯Ñ �� Ë ��ÒÓÓÔ

� 6.54

ℎ'(),-. = N'U'�~I + ~(1u��~I� + ~(1u� � 6.55

6.1.1.7 Surface area consideration

The surface area exposed to the drying gas stream influences the drying rate. In a study, the

contact surface area was assumed to be equal to the sum of the particle area of the suspended

mass in the flighted rotary dryer (Didriksen, 2002). However, the accurate estimation of this

surface area without experiments can be difficult because of the effect of the dryer operating

conditions and the solid properties such as the particle size, void fraction and cohesion.

In unflighted dryers, the surface area in contact with the gas largely depends on the solids bed

motions within the drum. The solids bed motion is dependent on the rotational speed and internal

geometry of the dryer. The solids move in different modes: rolling, slipping and slumping

(Mellmann, 2001). The most common solid movement in an industrial rotary drum is the rolling

mode because of its low rotational speed. Consequently, this study assumed that the rolling mode

occurs in the unflighted sections. Studies have shown that the rolling mode is characterised by

two distinct regions: active layer and passive layer. The active layer is characterised by vigorous

mixing of particles and hence a high rate of surface renewal which promotes heat transfer. In the

passive region, it is commonly assumed that little or no mixing occurs. The estimation of the

142

thickness of the active layer has been a subject of interest for researchers (Boateng, 1993; Jauhari

et al., 1998; Mellmann et al., 2004; Liu et al., 2006). There may be a need for a correction factor

to address the uncertainty in the theoretical estimation of these surface areas in both the

unflighted and the flighted sections of the dryer.

6.1.1.7.1 Unflighted section

In the unflighted sections, convection, radiation and evaporation are assumed to occur. However,

unlike the airborne solids, the available area is assumed to be reduced. Heinen et al. (1983a)

measured the thickness of the active layer to be less than eight particle diameters. Previous

studies have also modelled the active layer as a thin layer with the assumption of flat bed surface

(Ding et al, 2001; Heydenrych et al., 2002). The difference in the experimental observations by

Heinen et al (1983a) and the latter modelling approach clearly shows that the estimation of the

thickness of the active layer remains ambiguous. As a result, this study assumed a single particle

diameter as the depth of the active layer and a correction factor was introduced to address the

uncertainty in the assumption. The implications of this assumption are discussed in Section 6.2.1.

Thus, to determine the surface area of solid particles in contact with the gas stream within the

active layer (Figure 6.4) and Equations 6.56–6.61 were used in the calculation.

143

Figure 6.4: Active layer and passive layer in the kilning section (AAL is area of active layer,

Akiln is the chordal area (kilning area))

Referring to Figure 6.4, to determine the kilning angle�OV�, the drum mass (both active layer and

passive layer) was converted to the chordal area (Akiln) using Equation 6.56 (Britton et al., 2006).

The area of the active layer was calculated using Equation 6.57. In this thesis, the thickness of

the active layer was assumed to be the diameter of a particle.

5V"Q#T = �V"Q# = ��2 �OV − sin OV� 6.56

�²Ö = m� × �� 6.57

where 5V"Q#, OV , m� and �� are kilning mass (kg/m), kilning angle (radian), chordal length (m)

and particle diameter (m) respectively.

The mass of the active layer (both solid particles and void) was determined using Equation 6.58.

Active layer

Passive layer

OV

Akiln

AAL

Lc

144

7²Ö = ` �²Ö�V"Q#c × �5� × ∆K� 6.58

where 5� , ∆K are the mass of solid in each cell (kg/m) and length of the discretised cell (m)

respectively. The length of the discretised cell was calculated using Equation 6.59

∆K = m :�� 6.59

where m, :� are length of the unflighted section and number of discretised cells respectively.

The surface area of the estimated active layer in contact with the gas stream was then calculated

by determining the number of solid particles within the active layer. It is then assumed that half

of the total surface area of a solid particle is exposed to the gas stream (Equation 6.60).

�²Ö = 7²Öª4 3� ��0.5��¯ T�& �4��0.5��2 6.60

where T× is the density of a particle.

Because of the uncertainty in estimating surface area, a correction factor (θAL) is introduced,

(Equation 6.61). The estimation of θAL will be discussed in the parameter estimation section.

�²Ö = O²Ö ¹ 7²Öª4 3� ��0.5��¯ T�& �4��0.5��2 ¾ 6.61

where θAL is the correction factor for the surface area of solid particles in the active layer.

6.1.1.7.2 Flighted section

As the solids cascade through the gas stream, there are voids within the falling solid particles. To

determine the surface area (Aa) of airborne (or active) particles in contact with the gas stream, the

145

number of solid particles was calculated. It is then assumed that half of the surface area of a

particle was exposed to the gas stream (Equation 6.62). A correction factor (θa) was also

introduced to account for uncertainty in the estimated surface area. For future study, CFD

analysis can also be used to determine the void fraction within the airborne solids.

�( = 7(ª4 3� ��0.5��¯ T�& �4��0.5��2 6.62

With the inclusion of the correction factor (θa), Equation 6.62 becomes:

�( = O( ¹ 7(ª4 3� ��0.5��¯ T�& �4��0.5��2 ¾ 6.63

6.2 Model solution

The model equations in Section 6.1 were solved using gPROMS modelling software. gPROMS

code for this study can be found in Appendix F. Parameter estimation was carried out using the

RTD and the moisture content profiles of the operating conditions presented in Table 6.1 (Test

4). The operating conditions represent the ideal condition of the dryer because the data were

collected immediately after internally cleaning of the dryer and the operating conditions were

close to its original design criteria. The predictability of the model was further tested by using

these estimated values under the conditions of Tables 3.8, 3.10– 3.11. The mean particle sizes

presented in Section 3.4.3 were used in the estimation of the solid surface area in contact with

the gas stream in different sections of the dryer. As a result, the assumed mean particle diameters

for sections A,B,C,D and E in the dryer were 0.02 m, 0.015 m, 0.012 m, 0.008 m, 0.007 m

respectively. The gas properties such as density, thermal conductivity and dynamic viscosity

146

were modelled as a function of gas temperature (Incropera & DeWitt, 2002). The specific heat

capacity of the water vapour was also modelled as a function of operating temperature (Incropera

& DeWitt, 2002).




Gas inlet temperature 500 oC 16.05 oC



Product outlet temperature 46 0C 0.4 oC





6.2.1 Parameter estimation

The scaled moisture content profile shown in Figure 6.5 was the key experimental data used for

model parameter fitting. The surface area correction factors (θAL and θa) in Equations 6.61 and

6.63 were used for parameter estimation. The parameter estimation was done manually because

of the complexity within the model that resulted in numerical instability and significant

computing requirements.

147

Different approaches were taken to investigate the dependence on these terms. The correction

factor was assumed to be constant across the different sections of the dryer, which indicates a

degree of confidence in both theoretical approaches to surface area determination. The fitted

moisture content profile shown in Figure 6.5 was based on constant area correction factors (θAL

and θa) equal to 1 (no correction factor) and 1.3 (constant correction factor). Both approaches

resulted into poor fitting of the experimental moisture content data. It can be seen from the graph

that without suitable correction factors, the fitting of the solid moisture content profile of the

dryer was difficult (Figure 6.5).

To improve the fit to the moisture content profile, different correction factors were used for the

different sections of the drum. The correction factors were obtained by manually tuning to fit the

moisture content profile. The manually tuned surface area correction factors for the unflighted

sections (A and E) were 2.4 and 1.4, which could indicate that the active layer is more than one

particle diameter thick. However, the true thickness of the active layer is difficult to define

accurately because of the complexity of the drying mechanism. The correction factors for the

flighted sections B, C and D were 1.2, 0.6 and 0.42 respectively. It can be deduced from Figure

6.6 that the loss of moisture occurred mostly in the flighted sections but at the unflighted sections

of the dryer, the evaporation rate was reduced. The difference in evaporation rate in the different

sections can also be attributed to the amount of solids in contact with the incoming gas. The

estimated interfacial surface areas for flighted sections B, C and D were 0.086 m2/kg, 0.054

m2/kg and 0.056 m2/kg respectively while for the unflighted sections A and E were 0.0047 m2/kg

and 0.0029 m2/kg. The small interfacial area at unflighted sections of the dryer indicated minimal

drying. This observation further established the assumption of negligible drying in the passive

phase of the flighted sections.

148

In order to match the gas outlet temperature, the heat loss correction factor in Equation 6.50 was

also manually tuned but was assumed to be a constant value across the dryer. The manually

tuned value was 15.

Figure 6.5: Effect of area correction factor on moisture content profile

0.1

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0 5 10 15 20So

lid

mo

istu

re c

on

ten

t (k

g/k

gw

et s

oli

d)

Axial position in the dryer (m)

Experimental data

Without area correction factor

Constant area correction factor

149

Figure 6.6: Solid moisture content profile

6.3 Model verification

To verify the model, mass and energy balances across the dryer were examined. Under steady

state conditions, both mass and energy were conserved. For further verification, the mass of the

tracer leaving the dryer was also compared to the mass of the tracer added to the dryer. The mass

of the tracer that exited from the dryer was equal to the mass of the tracer added to the dryer.

Figure 6.7 shows the predicted RTD profile well matched to the experimental RTD data.

0.12

0.13

0.14

0.15

0.16

0.17

0 5 10 15 20

So

lid

mo

istu

re c

on

ten

t (k

g/k

gw

et s

oli

d)

Axial position in the dryer (m)

Experimental data

Predicted data

150


The internal gas and solid temperature profiles across the dryer were not available and as a

result, the study assumed if the outlet predicted values agree with the experimental values, the

predicted profile was assumed to be appropriate. Figures 6.8 and 6.9 show the solid temperature

profile, and gas and shell temperature profiles respectively.

0

10

20

30

40

50

60

650 750 850 950 1050 1150 1250

Tra

cer

con

cen

tra

tio

n (

pp

m)

Time (seconds)

Experimental RTD

Simulated RTD

151

Figure 6.8: Solid temperature profile (Test 4)

Figure 6.9: Gas and shell temperature profiles (Test 4)

25

30

35

40

45

50

0 5 10 15 20

So

lid

te

mp

era

ture

(oC

)

Axial poistion in the dryer (m)

0

20

40

60

80

100

120

140

160

120

180

240

300

360

420

480

540

0 5 10 15 20

Sh

ell

tem

per

atu

re (

oC

)

Gas

tem

per

atu

re

(oC

)

Axial position (m)

Gas temperature

Shell temperature

152

The model was further tested using the operating conditions presented in Tables 3.8, 3.10–3.11.

The predicted values of product moisture content, product temperature and gas outlet

temperature are presented in Tables 6.2–6.4. The predicted values of product moisture content

and product temperature at different operating conditions were comparable with the experimental

data demonstrating the strong predictability of the model. There is some discrepancy in the gas

outlet temperature but the trends are consistent.

Table 6.2: Product moisture content

Experimental value

(kg/kgwet solid)

Predicted value

(kg/kgwet solid)

Test 3 0.136 0.143

Test 5 0.12 0.116

Test 6 0.122 0.127

Table 6.3: Product temperature

Experimental value

(oC)

Predicted value

(oC)

Test 3 46 41

Test 5 45 47

Test 6 47 48

153

Table 6.4: Gas outlet temperature

Experimental value

(oC)

Predicted value

(oC)

Test 3 165 168

Test 5 155 137

Test 6 150 130

6.4 Summary

A dynamic multiscale model was developed and validated for an industrial rotary dryer based on

the assumption that the predicted and measured outlet temperature values should be similar. In

order to facilitate the drying, the energy balances of both solid and gas phases were incorporated

into the validated solid transport model presented in Chapter 5. The gas phase in both unflighted

and flighted sections was modelled as plug flow systems. The correction factors were introduced

to account for the uncertainty in the estimated surface areas of solids at different sections of the

dryer. These correction factors were manually parameter estimated using the experimental

moisture content. The heat loss via the shell was calculated using the resistance analysis. In order

to match the gas outlet temperature, a heat loss correction factor was also introduced and was

manually tuned.

154

CHAPTER SEVE

7. MODEL APPLICATIO

The key issues for MMG dryer management are those of controlling outlet moisture content,

controlling outlet solids temperature and optimising fuel economy. The generation of solutions to

these issues is complicated by the progressive scaling that occurs within the dryer, which leads to

changing dryer performance over time. It is clear that complex multiscale dynamic dryer models,

such as that developed in this thesis, are well suited to informing the development of control

schemes, assisting the understanding of these complexities and predicting the effects of scaling

on dryer outputs. In this chapter, the dynamic dryer model developed in Chapter 6 was utilised to

gain insight on how to operate the dryer at both unscaled and scaled conditions and to provide

insight into the complexities of drying. As a result of observations, the model was further used to

investigate potential solutions to maximize heat retention within dryer and to reduce fuel

consumption.

A typical dryer control scheme consists of three main factors: manipulated variables, controlled

variables and disturbance variables. Currently, a distributed control system (DCS) based on feed

forward control is used to control the MMG rotary dryer. The control algorithm calculates the

amount of water to be removed from the solid using the following operating variables: solid inlet

and target product moisture content, solid feed rate and air flow into the combustion chamber.

The estimated amount of water is then used to determine the amount of fuel oil required for the

combustion process, in effect increasing the gas inlet temperature. Scaling is not accounted for in

MMG’s control schemes. Despite the current control strategy, there is significant variation in the

product moisture content due to changes in the solid feed rate and inlet moisture content, which

155

largely depends on the operation and performance of the five batch filter presses preceding the

drying process.

The scale build-up within the dryer also affects the product quality because the gas-solids

interaction is reduced in a scaled dryer (as observed in Section 5.4.1.1) and to compensate,

MMG increases their fuel consumption in order to achieve product quality targets. It should be

noted that the increase in fuel consumption is based on operator’s judgment and experience.

Despite the significant increase in fuel consumption, the desired product quality is commonly not

achieved. Therefore, it is evident that there is a need to gain insight into the process performance

under scaled and unscaled operations using the developed dynamic model.

To operate the dryer at an optimum condition, it is vital to identify the most suitable

manipulated variables for different operating conditions. In this work, the suitability of a

manipulated variable is defined by the following characteristic: can be adjusted in order to

maintain the controlled variable at its set value. To identify the manipulated variable, the

approach developed by Duchesne et al. (1997) was used. The approach measures the relative

indices of the outlet variables to changes in the inlet variables.

The operational issues associated with MMG rotary dryer are high fuel consumption and scale

build-up within the dryer. High fuel consumption results into significant increase in operating

cost and carbon dioxide emission into the environment. With the newly introduced carbon price

mechanism, it is important to investigate ways to reduce carbon pollution via reduction in fuel

consumption. A novel solution rapidly gaining momentum is to maximise the heat energy within

the dryer by insulating the outside shell. Prior to insulating dryers, the model should be used to

examine the shell temperature profile in order to avoid shell degradation and external

156

temperature measurements should be taken so as to verify these findings. The dynamic model

developed in this thesis provides an effective tool for examining potential benefits and

identifying thermal constraints.

7.1 Relative indices analysis

The manipulated variables were identified using an approach used in a similar dryer modelling

study by Duchesne et al. (1997). The approach involves determining the relative indices of the

output variables to changes in the input variables using Equation 7.1. The significance of relative

index was determined by how large its magnitude is in either a negative or positive direction. For

example, a large positive relative index indicates that either increases or decreases in input

variables will have significant effect on the corresponding output variables.

Ø = �Ù − Ù'6;� Ù'6;��Ú − Ú'6;� Ú'6;� 7.1

here Ø is the relative index, Ù'6; and Ù are the values of the output variables before and after

the change respectively. Ú'6; is the initial value of the input variable and Ú is its new value.

Five input variables were changed consecutively and their effects on product moisture content

and product temperature were monitored. In this analysis, the temperature units were taken as

degrees centigrade. The following input variables were selected for investigation: gas inlet

temperature, gas inlet humidity, dryer’s rotational speed, solid inlet temperature and solid feed

rate. Gas inlet temperature is currently used as the manipulated variable in the industry control

scheme. Rotational speed greatly affects the solid residence time and active mass (as observed in

Section 5.4.1.2). Its potential as a manipulated variable was examined in this study. The gas inlet

humidity was considered because in the sugar industry, the inlet air is conditioned prior to its

157

introduction into the dryer. The prospect of solid temperature as a manipulated variable was

investigated because it contributes to the magnitude of the drying rate (Equation 6.33). It has also

been observed in sugar drying that steam is added to the inlet sugar in order to increase moisture

removal. This approach to dryer control may offer new opportunity to the mineral industry but

care must be taken to avoid storage issues associated with high solid temperature. The effect of

solid feed rate was investigated because the loading state plays a significant role in the efficiency

of the dryer. As observed in Section 5.4.1.1, the active mass reduces as the scale accumulation

increases. Therefore, reduction in solid feed rate may potentially be used to facilitate better gas-

solids interaction, particularly within a scaled dryer. However, the practicability of this option

remains to be examined (by the industry).

Product moisture content and temperature were considered as output (controlled) variables

because there is a need to maintain transportable moisture content limit (12%) for MMG’s

products. In addition, MMG’s current operating policy is to maintain product temperature within

the range of 45 oC to 50 oC so as to avoid internal movement of water molecules to the external

surface of the solid particles, which could lead to uncontrolled stickiness in the storage area.

In this study, the dryer’s internal scaling condition was examined across the range of 0% to 80%.

To obtain the references values, the steady state solutions from simulations carried out using the

operating conditions presented in Table 6.1 under scenarios of 0% scaled to 80% scaled. For an

overloaded scenario; the solid feed rate in Table 6.1 was changed to 63.89 kgwet solids/s. The

relative indices were determined by changing the specified input variable and performing the

new simulations. The gas inlet temperature and gas inlet humidity were varied by positive 10%

and negative 30% respectively. The solid inlet temperature and solid feed rate were varied by

changing its initial values by positive 30% and negative 20% respectively. The maximum

158

rotational speed limit for MMG rotary dryer is 3 rpm, thus it was varied by reducing the speed by

30%. The relative indices of the output variables are presented in Tables 7.1- 7.5. Note in these

tables that an increase in reference variable will result in a positive denominator in Equation 7.1

and a decrease will result in a negative denominator.

Table 7.1: Relative indices of output variables for a change in gas inlet temperature

Solid feed rate

(kgwet solid/s) Dryer condition

Product moisture

content

Product

temperature

40.64 0% scaled -0.425 0.410

40.64 40% scaled -0.354 0.379

40.64 60% scaled -0.287 0.387

40.64 80% scaled -0.228 0.390

63.89 0% scaled -0.284 0.375

Table 7.2: Relative indices of output variables for a change in gas inlet humidity

Solid feed rate


Product moisture

content

Product

temperature

40.64 0% scaled 0.030 0.092

40.64 40% scaled 0.025 0.103

40.64 60% scaled 0.025 0.120

40.64 80% scaled 0.026 0.141

63.89 0% scaled 0.019 0.074

159

Table 7.3: Relative indices of output variables for a change in rotational speed

Solid feed rate


Product moisture

content

Product

temperature

40.64 0% scaled 0.110 -0.094

40.64 40% scaled -0.092 0.093

40.64 60% scaled -0.056 0.071

40.64 80% scaled -0.023 0.037

63.89 0% scaled -0.089 0.116

Table 7.4: Relative indices of output variables for a change in solid inlet temperature

Solid feed rate


Product moisture

content

Product

temperature

40.64 0% scaled -0.053 0.084

40.64 40% scaled -0.044 0.082

40.64 60% scaled -0.043 0.097

40.64 80% scaled -0.041 0.115

63.89 0% scaled -0.040 0.096

Table 7.5: Relative indices of output variables for a change in solid feed rate

Dryer condition Product moisture

content

Product

temperature

0% scaled 0.198 0.124

40% scaled 0.337 0.0003

60% scaled 0.274 -0.008

80% scaled 0.211 -0.005

160

7.1.1 Discussion

The relative indices showed that the gas inlet variable temperature has most significant effect of

all inlet variables on both product moisture content and temperature (Table 7.1). The product

temperature responded to change in the gas inlet temperature in the opposite direction when

compared with product moisture content. This phenomenon indicates that the solid temperature

profile along the dryer is an important driving force in evaporative drying i.e. the higher the solid

temperature, the higher the evaporation rate. However, the relative indices presented in Table 7.4

showed that increasing the solid inlet temperature does not enhance drying rate to the same

extent. This observation demonstrates the complex relationship between the mechanisms

involved in the rotary drying process. As the scale build up increases within the dryer, there is

reduction in the effectiveness of using gas inlet temperature to control product moisture content,

which is assumed to be a result of loading state. It should be noted that increasing gas inlet

temperature in a scaled dryer increases the fuel consumption within the combustion chamber

without necessarily achieving the product specification. This has been also observed by MMG

operations controlling under high scaling situations. Similar conclusions can be made regarding

high solid feed rate scenarios, which also reduce the effectiveness of gas temperature as a

manipulated variable. The relative indices in Table 7.1 could be used to modify the existing

control strategies under these scenarios

Gas inlet humidity has a reduced effect on the output variables for the different operating

conditions compared to gas inlet temperature (Tables 7.2 and 7.3). Its effect is to decrease both

the solid outlet moisture content and temperature. Under scaled conditions, inlet gas humidity

could be used in conjunction with inlet gas temperature to better control the dryer. With 30%

decrease in the gas inlet humidity, the decrease in the exhaust gas humidity ranged from 5% to

161

8% for the studied conditions. It is evident that the driving force for drying the solid also

depends on the temperature difference between the gas and solids.

The effect of rotational speed on temperature and moisture presented in Table 7.3 is complicated.

Rotational speed affects both the residence time and the proportion of solids in the active and

passive phases. Lower speed results in more solids rolling on the base of the drum at both scaled

and overloaded conditions compared to unscaled condition. For example, in section B of the

dryer, the passive masses at different scaling conditions are: 1970 kg (0% scaling), 4006 kg (40

% scaling), 4400 kg (60% scaling) and 4600 kg (80% scaling). On the other hand, the active

mass decreases with increase in the scaling condition: 250kg (0% scaling), 194 kg (40% scaling),

125 kg (60% scaling) and 70 kg (80% scaling). It can be concluded that the increase in the

passive solids at different scaling conditions has an opposing effect to the increased residence

time resulting from decreased rotational speed. Intuitively these effects are hard to predict

without the use of models such as that developed in this thesis.

Table 7.5 shows that the loading state of the dryer (induced by varying solid feed rate) has

significant effect on the product moisture content. Solid feed rate as a manipulated variable for

scaled conditions is a potential solution to achieving target product moisture content in

comparison to using the gas inlet temperature as manipulated variable. Similar to the

observations regarding rotational speed, a predictive model is considered essential to

implementing this approach. However, the practicability of this option largely depends on the

production targets of the industry.

162

7.2 Optimising fuel consumption

The gas inlet temperature was recognized in the previous section to be one of the most important

manipulated variables. The gas inlet temperature to the dryer is manipulated by increasing fuel

consumption in the combustion chamber. The cost of fuel consumed is one of the major

operating costs for the MMG rotary dryer and typical rate of consumption is 750 kg/hr of fuel to

generate hot inlet gas temperature at 500 oC. With increasing cost of fuel and increased

emphasis on reducing carbon dioxide emission to the environment, the model is used to examine

engineering design options to reduce the daily fuel consumption.

It is a common practice in process industries to externally insulate the dryer so as to increase its

thermal efficiency and reduce heat losses. However, mild steel degradation can occur when wall

temperatures exceed 593 oC (according to API standard 521). This constraint is often used to

justify the absence of thermal insulation on dryer walls. The model can be easily manipulated

through minor adjustment in model parameters to represent such common engineering design

solutions. The model was used to investigate options to maximize the retention of heat within the

dryer. In the model developed in this thesis, the heat loss was assumed over the entire

circumference of the shell and was modeled by determining individual thermal resistances

through the shell as stated in Equation 6.50. To examine the option of externally insulating the

dryer, the heat loss factor in Equation 6.50 was set to zero, effectively removing completely heat

losses through the shell. The effect on output variables such as gas outlet temperature and

product moisture content was monitored.

Table 6.1 presents the operating conditions used for the investigation. Figure 7.3 presents gas

temperature profiles with and without heat loss. Figures 7.4 and 7.5 are the solids temperature

and moisture content respectively. The study observed a 90% and a 22% increase in the solid and

163

gas outlet temperatures respectively when the heat loss factor was set to zero. The increase in the

product temperature indicates that by insulating dryer shells, the convective heat transfer to

solids can be increased, which enhances the drying process and, leads to decrease in the product

moisture content. However, care must be taken to avoid increases in the product temperature

that can result in downstream storage problems.

Figure 7.1: Effect of external heat loss on gas temperature profile

0

100

200

300

400

500

600

0 5 10 15 20

Ga

s te

mp

era

ture

(oC

)

Axial position (m)

Heat loss

No heat loss

164

Figure 7.2: Effect of external heat loss on solid temperature profile

Figure 7.3: Effect of external heat loss on solid outlet moisture content profile

25

30

35

40

45

50

55

60

0 5 10 15 20

So

lid

tem

per

atu

re (

oC

)

Axial position (m)

Heat loss

No heat loss

0.09

0.11

0.13

0.15

0.17

0 5 10 15 20

So

lid

mois

ture

co

nte

nt

(kg/k

gw

et s

oli

d)

Axial position (m)

Heat loss

No heat loss

165

In an attempt to avoid high gas and solid outlet temperatures, the gas inlet temperature was

reduced for the insulated rotary dryer. Figures 7.6 and 7.7 show the resulting moisture profile

and solid temperature profile for a reduced inlet gas temperature (350 oC) respectively. The

figures illustrate a potential reduction in fuel consumption through external insulation of the

dryer whilst maintaining the desired product quality for the proposed externally insulated dryer.

The difference in the solid temperature and moisture profiles for heat loss and no heat loss

scenarios can be attributed to variation in gas temperature profiles along the length of the drum.

Another retrofit modification is to recycle back the exhaust gas from the dryer into the

combustion chamber, thereby further reducing the amount of fuel consumed within the dryer.

However, this option was not quantified in this current study.

Figure 7.4: Effect of gas inlet temperature on solid moisture content profile in an insulated

dryer

0.12

0.13

0.14

0.15

0.16

0.17

0 5 10 15 20

Soli

d m

ois

ture

co

nte

nt

(kg/k

gw

et

soli

d)

Axial position (m)

500 degrees Celsius(Heat loss)

350 degrees Celsius(No heat loss)

166

Figure 7.5: Effect of gas inlet temperature on solid temperature profile in an insulated

dryer

7.4. Summary

The most suitable manipulated variables under both scaled and unscaled conditions were

determined. The criterion for choosing a suitable manipulated variable was determined using the

approach developed by Duchesne et al. (1997). The approach measured the relative indices of the

outlet variables to changes in the inlet variables. The gas inlet temperature was found to be the

most suitable manipulated variable to control and optimise the drying process but its

effectiveness depends on scaling and loading states within the dryer. The model was found to be

necessary to understand the complex effects of rotational speed and gas humidity on output

variables. The study also suggested the solid feed rate be reduced for a scaled dryer (i.e.

modifying the loading state) so as to achieve optimum gas-solid interaction. To further utilize

the model to reduce the amount of fuel consumed, the study investigated options to maximize the

25

30

35

40

45

50

0 5 10 15 20

So

lid

tem

per

atu

re (

oC

)

Axial position (m)

500 degrees Celsius(Heat loss)

350 degrees Celsius(No heat loss)

167

retention of heat within the dryer. Although the model presents a simplified description of

thermal profile within a dryer shell, insulating the dryer coupled with reduction in the gas inlet

temperature appears to be a promising option for meeting the desired product quality and

reducing fuel consumption.

168

CHAPTER EIGHT

8. CO CLUSIO A D RECOMME DATIO S

8.1 Conclusion

A dynamic multiscale model was developed and validated for the MMG rotary dryer. The gas

phase in both the unflighted and flighted sections of the dryer was modelled as a plug flow

system. The solid phase in the unflighted sections was modelled as an axial dispersed plug flow

system. Following typical convention, a compartment modelling approach was used to model the

solid transport in the flighted sections. This approach is a series-parallel formulation of well-

mixed tanks and solids distribution between the compartments was estimated through geometric

modelling and consideration of design loading constraints. The modelling approach was able to

account for variation in flight configuration and geometry. Model parameters were estimated via

a combination of geometric modelling (flight geometry, dryer geometry and solid properties) and

parameter estimation.

Flight loading experiments were carried out at pilot scale to determine the effect of moisture

content and rotational speed on dryer design loadings. Multiple photographs of the cross-

sectional area of the drum were taken and analysed. The study developed an automated

combination of ImageJ and MATLAB code to enhance the image quality and to estimate the

regions of interest. The regions of interest were the first unloading flight, the upper half of the

drum, the total flight-borne solids and the airborne phase.

To determine the design loading, different approaches were investigated. The estimated design

load values based on all the approaches were similar, however, the piecewise regression analysis

of the saturated first unloading flight data were found to be more consistent, after consideration

169

of the error in the estimated values. Similar profiles were obtained using the approaches based on

the saturation of the airborne solids and of the flight-borne solids in the upper half of the drum.

The study observed a sudden peak in the plotted areas of the airborne solids and of the flight-

borne solids in the upper half of the drum. The peaks may be used as a criterion to estimate the

design load but require highly accurate determination of area and also an understanding of the

flight-borne solids bulk density. The design loading increased with an increase in moisture

content and an increase in rotational speed.

The mass of airborne solids at the design load was determined using a combination of image

analysis and Eulerian-Eulerian simulation of free-falling curtains. The airborne solids increase

with an increase in rotational speed but challenges with analysing high moisture content situation

remain. The study also carried out experimental validation of design load models available in the

literature and a modified equation based on the Baker (1988) model was proposed. The modified

design load model was used in this study as a constraint within the compartment model.

In order to validate the dynamic multiscale model of the dryer and parameter estimate unknown

model parameters, a series of residence time distribution (RTD) pulse tracer tests were

performed using lithium chloride as the tracer. Solid velocity and axial dispersion coefficients

were parameter estimated using the RTD experimental data. The experimental moisture content

profile was used for model parameter fitting. The gas and solid temperature profiles were also

predicted.

There was uncertainty in the estimation of the solid surface area in contact with the gas stream,

which led to introducing correction factors within the surface area terms for different sections of

the dryer. The correction factors were manually tuned to fit the experimental moisture content

170

profile. The study observed the interfacial surface areas at the unflighted sections were small in

comparison to the airborne solids, which indicated the gas-solids interaction in the kilning phase

was minimal. This observation validated the commonly made assumption of negligible drying in

the passive phase or kilning phase of the flighted sections of flighted rotary dryers.

The main manipulated variables for different operating conditions were identified using the

relative sensitivity indices of output variables to changes in the input variables. Gas inlet

temperature was identified as the manipulated variable for MMG rotary dryer. Both rotational

speed and gas inlet humidity have small effect on the output variables. At scaled internal

condition, the study suggested the solid feed rate should be reduced so as to achieve optimum

gas-solid interaction. To address high fuel consumption associated with MMG rotary dryer, the

study proposed the dryer should be externally insulated so as to maximize the thermal efficiency

of the dryer. It should be noted that mild steel degradation can occur when the dryer’s wall

temperature exceeds 593 oC. However, the wall temperature for the studied dryer is expected to

be less than 593 oC because the gas inlet temperature for the proposed externally insulated dryer

will be around 350 oC.

8.2 Recommendations

Based on the findings in this thesis, the following recommendations are made:

• This study observed a sudden peak in the airborne and upper flight-borne mass during the

flight loading experiments. To further investigate this phenomenon and also investigate

voidage variation in the airborne solids, there is a need to improve the experimental set-

up. These improvements include: reducing the length of the drum so as to avoid

background interference of the falling solid particles and the lighting set-up should be

171

improved so as to achieve consistent pixel intensity within a set of photographs for a

particular experimental condition.

• In this study, the geometric model calculates the cross-sectional area of flight-borne

solids and a consolidated density was assumed to determine the flight holdup. It is a

challenge to quantify density in both flights and in the airborne phase. There is need to

determine the density profile of flight-borne solids, which could be facilitated by

improved image analysis and more controlled particle properties.

• This study developed correlations for solid velocity and axial dispersion coefficient

correlations based on limited RTD experimental data. It is important to carry out a

comprehensive parametric study to determine how the operating parameters such as

rotational speed, dynamic angle of repose, diameter of the drum and loading state of the

drum affect the residence time and axial dispersion in the kilning phase. These RTD

experiments should be carried out on pilot scale dryer because of the complexity involved

in manipulating the operating variables within an industrial setting.

• There is a need for better understanding of the dynamics of the gas phase. Residence time

distribution tests for the gas phase in flighted rotary dryers should be undertaken in

conjunction with collection of velocity and high quality humidity measurements.

• In literature, there is no heat transfer correlation developed for curtaining particles. An

experimental and CFD study needs to be undertaken to investigate heat transfer

mechanism within the curtains. The study can provide information on how to model the

heat transfer coefficient in the multiscale model and provide greater certainty regarding

airborne solid interfacial contact areas. There is also a need to investigate the complex

172

relationship between the evaporation rate and the convective heat transfer as observed in

this study as this is critical to dryer control.

• A dynamic model was developed but there was uncertainty in the responses of the outlet

variables to step change in the inlet parameters. Thus, a validation of the dynamic

response is required through the collection of dynamic data from the Process Information

(PI) data.

173

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184

APPE DI CES

APPE DIX A: COMBUSTIO CHAMBER

The air enters the combustion chamber and is heated by burning the fuel oil. The hot gas leaves

the combustion chamber at an approximate temperature of 500 0C. The gas flow rate into the

dryer is not measured directly. This section presents the mass balances around the combustion

chamber to determine its value.

Figure A1: Block diagram of the combustion chamber

COMBUSTIO

CHAMBER

Dilution air

Relative humidity (kmol/kmol)

Temperature (oC)

Oxygen (XDO)(%kmol)

Nitrogen (XD,)(%kmol)

Molar flow rate (MD)(kmol/hr)

Hot gas

Moisture content � ÛÜÝÞ�(kmol/kmol)

Carbon dioxide � ÛßÞÝ� (kmol/kmol)

Sulphur dioxide � ÛàÞÝ� (kmol/kmol)

Nitrogen� ÛáÝ�(kmol/kmol)

Molar flow rate (Mg) (kmol/hr)

Fuel oil

Moisture content (XFw)(kg/kg)

Carbon (XFC)(kg/kg)

Hydrogen(XFH)(kg/kg)

R (mole C/mole H)

Sulphur (XFS) (kg/kg)

Mass flow (MF)(kg/hr)

Combustion air

Relative humidity (kmol/kmol)

Temperature (oC)

Oxygen (XDO(kmol/kmol)

Nitrogen (XD,(kmol/kmol)

Molar flow rate (MC)(kmol/hr)

185

Air properties

Arbuckle and Brash (2001) carried out experimental measurements in 2001 to determine the

relationship between the percentage of the fan opening (PI data) and the experimental volumetric

flow rate (Figures A2 and A3). Fitted Equations A1 and A2 were used to determine the

volumetric flow rates for dilution air and combustion air respectively.

Figure A2: Dilution air (Arbuckle and Brash, 2001)

y = 951.5x + 8662R² = 0.9974

35,000

40,000

45,000

50,000

55,000

30 32 34 36 38 40 42 44 46

Vo

lum

etri

c fl

ow

rate

( m

3/h

r)

Fan opening(%)

186

Figure A3: Combustion air (Arbuckle and Brash, 2001)

951.5j + 8662 A1

209.95j + 6283.4 A2

Table A1: Fan opening and volumetric flow rate

Fan opening (%) Amount( m3/hr) kmol/hr

Dilution air 83.43 88050 3928

combustion air 15.80 23698 1057

The moisture content of dilution and combustion air were calculated based on the relative

humidity and temperature of air when the RTD experiments were undertaken (BOM, 2010).

Equation A3 was used to estimate the moisture content (kmol of water/kmol dry air).

y = 209.95x + 6238.4R² = 0.999

12,000

13,000

14,000

15,000

16,000

17,000

30 35 40 45 50

Vo

lum

etri

c fl

ow

ra

te(

m3/h

r)

Fan opening(%)

187

jDâ = <"ãEä< A3

<"ãEä = �ℎ100 × <"ãEä∗ A4

<"ãEä∗ is the vapour pressure at the air temperature obtained from the vapour pressure table(Felder

and Rousseau, 2005). <"ãEä , <, �ℎ are vapour partial pressure, atmospheric pressure (assumed to

be 1 atm) and relative humidity respectively.

Recycled oil properties

The composition of the recycled fuel oil is stated in Table A2 and was based on the data

presented in Bladwin (2005). The mass flow rate of the fuel oil was obtained from the Process

Information (PI) data.

Table A2: Composition of Recycled fuel oil

Content

Water content 0.35 wt%

Sulphur content 0.95 wt%

Carbon to Hydrogen(C:H) 7.6 (mol/mol)

Hot gas

Elemental mass balances were carried out to determine the composition and molar flow rate of

the hot gas leaving the unit. Carbon:

0 = 7\�\D − 73 �D9E7æD9E � 7æ�7æD9E� ` 1 25xy � 1 25xy �ç�c A5

Hydrogen:

188

0 = 7\�\0 + 7\�\â7æ0E9 ` 218c + �7� + 7P��Dâ7æ0E9 ` 218c− 73 �0E97æ0E9 ` 218c

A6

Nitrogen:

0= �7� + 7P��P� − 73 ��E A7

Sulphur:

0 = 7\�\F − 73 �F9E�32� A8

Oxygen:

0 = �7� + 7P��I7æ0E9 � 7æ9E7æ0E9� ` 1 25xy ç�1 25xy ��çc + �7�

+ 7P��P9E7æ9E `2 25xy ç�1 25xy ç�c+ 7\�\â � 7æ9E7æ0E9� ` 1 25xy ç�1 25xy ��çc− 73 �0E97æ0E9 � 7æ9E7æ0E9� ` 1 25xy ç�1 25xy ��çc− 73 �D9E7æD9E � 7æ9E7æD9E� ` 2 25xy ç�

1 25xy �ç�c− 73 �F9E7æF9E � 7æ9E7æF9E� ` 2 25xy ç�

1 25xy ç�c

A9

Total components in hot gas (Mg) stream

�F9E + �D9E + �0E9 + ��E = 1 A10

189

APPE DIX B: RTD DATA (Lithium concentration as a function of time)

TEST 1

Time

(minutes)

Concentration

(kg/kg)

2 0.202

5 0.237

9.5 1.16

10 0.86

10.5 3.37

11 6.88

11.5 6.44

12 14

13 17.5

13.5 22.9

14 13.1

14.5 10

15 5.02

15.5 3.31

16 2.76

16.5 2.65

18 1.25

20 0.743

190

TEST 2

Time

(minutes)

Concentration

(kg/kg)

Time

(minutes)

Concentration

(kg/kg)

2 0.462 14.5 2.66

4 0.976 15 2.18

5 0.412 15.5 1.27

6 0.928 16 1.07

7 1.12 16.5 0.881

7.5 0.993 17 1.009

8 0.991 18 0.963

8.5 1.18 19 1.13

9 1.1 20 0.362

9.5 2.1 25 0.974

10 3.53 30 0.972

10.5 9.16 35 0.963

11 14 45 1.01

11.5 21.1 60 1.08

12 31.8

12.5 18.2

13 15.8

13.5 7.83

14 3.57

191

TEST 3

Time

(minutes)

Concentration

(kg/kg)

Time

(minutes)

Concentration

(kg/kg)

Time

(minutes)

Concentration

(kg/kg)

3 0.259 13 18.8 40 0.259

3.5 13.5 22.4 45 0.293

4 0.314 14 21

4.5 0.31 14.5 17.9

5 0.289 15 10.6

5.5 0.383 15.5 6.2

6 0.255 16 4.38

6.5 0.721 16.5 2.51

7 1.03 17 2.09

7.5 0.0943 17.5 1.21

8 0.127 18 1.01

8.5 0.193 18.5 0.541

9 0.194 19 0.578

9.5 0.049 19.5 0.452

10 0.217 20 0.513

10.5 0.554 21 0.523

11 0.803 23 0.415

11.5 1.74 25 1.5

12 5.7 30 0.273

12.5 9.38 35 0.121

192

TEST 4

Time

(minutes)

Concentration

(kg/kg)

Time

(minutes)

Concentration

(kg/kg)

Time

(minutes)

Concentration

(kg/kg)

3 1.53 13 7.38 40 0.603

3.5 0.076 13.5 13.5 45 0.511

4 1.47 14 31.5

4.5 1.36 14.5 28.4

5 0.983 15 38.4

5.5 0.772 15.5 51.7

6 0.814 16 40.7

6.5 0.750 16.5 13.6

7 2.04 17 10.4

7.5 0.902 17.5 5.09

8 0.852 18 3.49

8.5 0.693 18.5 1.55

9 0.855 19 1.90

9.5 1.04 19.5 1.24

10 0.805 20 0.869

10.5 0.584 21 0.839

11 0.886 23 0.813

11.5 1.24 25 0.810

12 1.09 30 0.677

12.5 3.26 35 0.613

193

TEST 5

Time

(minutes)

Concentration

(kg/kg)

Time

(minutes)

Concentration

(kg/kg)

8 0.636 18 2.97

8.5 0.583 18.5 5.51

9 0.489 19 10.3

9.5 0.488 19.5 15.4

10 0.743 20 21.6

10.5 0.531 20.5 24.6

11 0.562 21 26.9

11.5 2.24 21.5 29.8

12 0.656 22 25.3

12.5 0.579 22.5 19.9

13 0.776 23 14.6

13.5 0.506 23.5 9.43

14 0.602 24 6.9

14.5 0.585 24.5 4.08

15 0.883 25 4.26

15.5 0.641 26 2.11

16 0.758 30 1.13

16.5 0.637 35 0.885

17 0.897 40 1.1

17.5 1.6

194

TEST 6

Time

(minutes)

Concentration

(kg/kg)

Time

(minutes)

Concentration

(kg/kg)

8 1.05 18 6.15

8.5 0.578 18.5 2.98

9 0.609 19 1.68

9.5 0.567 19.5 0.885

10 0.475 20 0.763

10.5 0.545 21 0.486

11 0.660 22 0.672

11.5 0.727 23 0.315

12 0.867 24 0.937

12.5 1.46 25 0.347

13 3.06 30 0.191

13.5 8.85 35 0.272

14 14.9

14.5 24.3

15 28.8

15.5 31.1

16 30.6

16.5 23.0

17 14.3

17.5 10.2

195

APPE DIX C: MATLAB CODE

%To calculate the area at 9 o' clock position

jpegFiles = dir('*.jpg'); % directory of pictures

for a = 1:length(jpegFiles) % loop to run large number of pictures

filename = jpegFiles(a).name;

data1 = imread(filename);

red = data1(:,:,1); % Extracting on

mass9 = red;

[m n] = size(mass9);

[I J] = meshgrid(1:n,1:m);

radiusa = 950; % Radius of the drum in the image(You can use imageJ software to determine)

Center =[2320,1250];

Circle = (I-Center(1)).^2 + (J-Center(2)).^2 >= radiusa^2; % To remove the active phase.

mass9(Circle) = 0;

radius = 815;%inner radius where the active phase lies(You can use imageJ software to

determine)

Center =[2330,1240];

Circle = (I-Center(1)).^2 + (J-Center(2)).^2 <= radius^2; % To remove the active phase.

mass9(Circle) = 0;

mass9(1315:2700,:)=0; % removing lower limit

mass9(1:1070,:)=0; % removing upper limit

mass9(:,1500:3700)= 0; % removing where there is no flight

nmass9=nnz(mass9);% number of pixels in the passive phase

196

imagesc(mass9)

len =(radiusa*2)/75; % the scale of pixel/cm

Area = len^2; % pixel/cm^2

mass9oclock = nmass9/Area;

y(a) = mass9oclock;

%disp(mass9oclock);%area @ 3 o clock position

end

FUF = y';

x = char(jpegFiles.name);

t = cellstr(x);

xlswrite('C:\nineoclockAreacalculation.xlsx', t, 'area', 'A1');

xlswrite('C:\nineoclockAreacalculation.xlsx', FUF, 'area', 'B1');

%To calculate the area of the upper half of the drum






upperpassive = red;

[m n] = size(upperpassive);



197

Center =[2320,1250];% center of the drum in the image(You can use imageJ software to

determine)

Circle = (I-Center(1)).^2 + (J-Center(2)).^2 >= radiusa^2; % Isolate the drum

upperpassive(Circle) = 0;


determine)

Center =[2330,1240];% center of the drum in the image(You can use imageJ software to

determine)


upperpassive(Circle) = 0;

%upperpassive(1:700,:)=0;

upperpassive(700:2700,:)=0;% removing lower half of the drum

upperpassive(:,2800:3700)= 0; % removing where the flights are empty

nupperpassive=nnz(upperpassive);% number f pixels in the passive phase

imagesc(upperpassive)

len = (radiusa*2)/75; % the scale of pixel/cm


upperpassive= nupperpassive/Area;

u(a) = upperpassive;

end

UHD = u';


t = cellstr(x);

198

xlswrite('C:\UHDAreacalculation.xlsx', t, 'area', 'A1');

xlswrite('C:\UHDAreacalculation.xlsx', UHD, 'area', 'B1');

%To calculate the area of the lower half of the drum






lowerpassive = red;

[m n] = size(lowerpassive);



Center =[2320,1250];%center of the drum in the image(You can use imageJ software to

determine)

Circle = (I-Center(1)).^2 + (J-Center(2)).^2 >= radiusa^2; % Isolate the drum

lowerpassive(Circle) = 0;


determine)

Center =[2330,1240];%center of the drum in the image(You can use imageJ software to

determine)


lowerpassive(Circle) = 0;

199

lowerpassive(1:700,:)=0; %removing the upper half of the drum

lowerpassive(:,2800:3700)= 0; % removing where the flights are empty

nlowerpassive=nnz(lowerpassive);% number of pixels in the passive phase

imagesc(lowerpassive) % image showing lower half of the drym

len = (radiusa*2)/75; % the scale of pixel/cm


lowerpassive = nlowerpassive/Area;

l(a) = lowerpassive;

%totalpassive = upperpassive + lowerpassive; % total passive area of the drum

end

LHD = l';


t = cellstr(x);

xlswrite('C:\LHDAreacalculation.xlsx', t, 'area', 'A1');

xlswrite('C:\LHDAreacalculation.xlsx', LHD, 'area', 'B1');

200

APPE DIX D: MATLAB CODE FOR ESTIMATI G DESIG LOAD

sslm = slmengine(x,y,'knots',3,'rightslope',0,'degree',1,'interiorknots','free','plot','on')

xlabel('Loading condition(kg)'), ylabel('Area of 3 o clock, cm^2')

c = sslm.knots(2)

slmeval(c,sslm)

slmeval(x,sslm)

201

APPE DIX E: CO FIDE CE I TERVAL OF DESIG LOAD

Figure E1 shows the piecewise regression analysis of FUF area data. The breaking point of

piecewise regression analysis was regarded as the design load discussed in Section 4.4.4. The

confidence interval of estimated design load is discussed below.

Figure E1: Design load estimation

The two lines in the above graph are represented by two different equations:

Gu = �uj + �u E1

G( = �(j + �( E2

Equations E1 and E2 represent the equations of the lines before and after the break point

respectively

�u is the slope of the line before the break point

�( is the slope of the line after the break point and this was constrained to zero.

�u is the intercept of the line before the break point

0

5

10

15

20

25

30

35

0 10 20 30 40 50 60

Are

a a

t F

UF

(cm

2)

Loading condition(kg)

Experiment Fitted data

202

�( is the intercept of the line after the break point and this was average of the data points after

the break point

The break point (B) is design load value and it can be derived from the two equations by subbing

x for B for the Equations E1 and E2. This gives Equation E3:

�uè + �u = �(è + �( E3

Therefore

è = �( − �u�u − �( = È� E4

The standard error of B (design load) was estimated based on the rule of propagation of errors as

stated in Equation E5.

{Ì = è × d�` {éÈ c� + ` {0� c� f E5

here {é , {0 are the standard errors of G and H in Equation D4 and they were obtained based

on the principle of propagation of errors.

Therefore, the 95% confidence interval for the design load is ê. ëì í àîï

The standard error of G was calculated as follows,

{é = �`{�(�( c� + `{�u�u c� E6

here {�(, {�u are the error in intercepts before and after the break point(design load)

respectively.

Similarly for H,

203

{0 = �`{²u�u c� + `{²(�( c� E7

here {²u, {²( are the error in slope before and after the break point (design load) respectively.

It should be noted that the error in slope after the break point is zero.

204

APPE DIX F: gPROMS Code

Process model

UNIT

D AS Dryer_Clean

PARAMETER

L1 AS REAL # Length of 1st Stage (m)

L2 AS REAL # Length of 2nd Stage (m)

L3 AS REAL # Length of 3rd Stage (m)

L4 AS REAL # Length of 4th Stage (m)

L5 AS REAL # Length of 4th Stage (m)

R AS REAL # Drum Radius (m)

theta AS REAL # Inclination of Drum (degrees)

# Flight Geometry in 3rd Stage of Dryer

Nf_2 AS INTEGER # No. Flights

s1_2 AS REAL # Flight Length 1


alpha1_2 AS REAL # Flight Angle 1


# Flight Geometry in 4th Stage of Dryer





205







N2 AS INTEGER # No. Cells in Section 2



Cp_w AS REAL # Specific heat capacity of water

Cp_z AS REAL # Specific heat capacity of zinc

landa AS REAL # Heat of vaporisation

Cp_air AS REAL # Specific capacity of air

P AS REAL # Pressure within the dryer

rho_p AS REAL # particle density of zinc

MONITOR

D.O.T_ppm;

D.O.tau;

D.O.T_flow;

D.C1.me;

D.C2(*).P.x_p;

D.C3(*).P.x_p;

D.C4(*).P.x_p;

206

D.C6.me;

D.C1.tair;

D.C2(*).AIR.T_airout;



D.C6.tair;

D.C1.H_out;

D.C2(*).AIR.H_out;

D.C3(*).AIR.H_out;

D.C4(*).AIR.H_out;

D.C6.H_out;

D.C1.ts;

D.C4(*).P.tp;

D.C3(*).P.tp;

D.C2(*).P.tp;

D.C6.ts;

D.Energy;

D.Energy_1;

D.Energy_2;

D.Energy_3;

SET

L1 := 2.1;

L2 := 2.4;

207

L3 := 3.6;

L4 := 6.6;

L5 := 7.5;

R := 1.95;

theta := 4;

Cp_w := 4182;

Cp_z := 505;

Cp_air :=1070;

landa :=(2257*1000);

rho_p := 2800;

P := 101045;

# Flight Geometry in 3rd Stage of Dryer

Nf_2 := 30;

s1_2 := 0.120;

s2_2 := 0.21;

alpha1_2:= 90;

alpha2_2:= 135;

# Flight Geometry in 4th Stage of Dryer

Nf_3 := 30;

s1_3 := 0.130;

s2_3 := 0.220;

alpha1_3:= 90;

alpha2_3:= 150;

208

Nf_4 := 30;

s1_4 := 0.120;

s2_4 := 0.210;

alpha1_4:= 90;

alpha2_4:= 130;

#Number of cells

N2 := 8;

N3 := 12;

N4 := 22;

ASSIGN

D.F_ain := 112675.6688; # Gas flow rate into section 1 and used as correlation for section 5

D.C1.H_ain := 0.0193; # Gas inlet humidity

D.C1.T_airin :=500; # Gas inlet temperature

D.Tamb :=26; # Ambient temperature

D.C1.F_k_in := 146320/3600; # Solid mass flow rate

D.C1.T_k_in := 0; # Tracer concentration

D.C1.u:=0.01557; # kilning time

D.C1.x_in:=0.163; # Solid moisture content

D.C1.tink:= 28; # solid temperature

D.omega :=3;

D.y := 0.000399686; # axial dispersed coefficient

D.f :=2.4; # area correction factor for section A

D.ha := 1.2; # area correction factor for section B

209

D.hb :=0.6; # area correction factor for section C

D.hc := 0.42; # area correction factor for section D

D.n :=1.4; # area correction factor for section E

D.lo_factor :=15; # heat loss correction factor for all sections

INITIAL

D.O.T_flow = 0;

D.O.xtime = 0;

D.O.tau = 0;

FOR i := 0|+ TO L1|- DO

D.C1.r(i) = (32250/D.L)*L1;

D.C1.T(i) = 0;

D.C1.me(i) = 0.168;

D.C1.Ts(i) = 25;

D.C1.Air(i) = (D.C1.F_ain/3600)/D.C1.v_g(0);

D.C1.tair(i) =500;

D.C1.H_out(i) = 0.0193;

END

FOR i:= 1 TO N2 DO

D.C2(i).P.m_p = (32250/D.L)*(L2/N2);

D.C2(i).P.T_p = 0;

D.C2(i).P.x_p = 0.15;

D.C2(i).P.tp = 32;

D.C2(i).A.m_a = (4/D.L)*(L2/N2);

210

D.C2(i).A.T_a = 0;

D.C2(i).A.x_a = 0.15;

D.C2(i).A.ta = 30;

END

FOR i:= 1 TO N3 DO

D.C3(i).P.m_p = (32250/D.L)*(L3/N3);

D.C3(i).P.T_p = 0;

D.C3(i).P.x_p = 0.14;

D.C3(i).P.tp = 32;

D.C3(i).A.m_a = (4/D.L)*(L3/N3);

D.C3(i).A.T_a = 0;

D.C3(i).A.x_a = 0.14;

D.C3(i).A.ta = 30;

END

FOR i:= 1 TO N4 DO

D.C4(i).P.m_p = (32250/D.L)*(L4/N4);

D.C4(i).P.T_p = 0;

D.C4(i).P.x_p = 0.13;

D.C4(i).P.tp = 35;

D.C4(i).A.m_a = (4/D.L)*(L4/N4);

D.C4(i).A.T_a = 0;

D.C4(i).A.x_a = 0.13;

D.C4(i).A.ta = 35;

211

END

FOR i := 0|+ TO L5|- DO

D.C6.r(i) = (32250/D.L)*L5;

D.C6.T(i) = 0;

D.C6.me(i) = 0.125;

D.C6.Ts(i) = 40;

D.C6.Air(i) = D.C4(N4).AIR.A_out/D.C4(N4).AIR.v_g;

D.C6.tair(i) = 120;

D.C6.H_out(i) = 0.1;

END

SOLUTIONPARAMETERS

LASolver := "MA28"

DASolver := "DASOLV"

REPORTINGINTERVAL :=10

#gExcelOutput := "checkit.xls" ;

SCHEDULE

# Method 1

#CONTINUE FOR 3600

# Tracer Study

SEQUENCE

CONTINUE FOR 1500

RESET

212

D.C1.T_k_in :=1.255E-04; # IMPORTANT: If you change this you need to change the

value in the Dryer Model as well.

END

CONTINUE FOR 60 # IMPORTANT: If you change this you need to change the value in the

Dryer Model as well.

RESET

D.C1.T_k_in := 0;

END

CONTINUE FOR 2500

END

#Dynamic studies

{SEQUE?CE

CO?TI?UE FOR 3500

RESET

#D.C1.F_k_in :=60000/3600;

# D.F_ain := 60000;

#D.C1.T_airin :=350;

#D.C1.H_ain := 0.002;

#D.C1.tink:= 25; # solid temperature

#D.C1.x_in:=0.15 ; # Solid moisture content

# D.omega:=2;

E?D

213

CO?TI?UE FOR 4500 # IMPORTA?T: If you change this you need to change the value in

the Dryer Model as well.

E?D}

214

Dryer Model

PARAMETER

N2 AS INTEGER # Number of cells in Section B

N3 AS INTEGER # Number of cells in Section C

N4 AS INTEGER # Number of cells in Section D

L1 AS REAL # Length of Section A

L2 AS REAL # Length of Section B

L3 AS REAL # Length of Section C

L4 AS REAL # Length of Section D

L5 AS REAL # Length of Section E

Cp_w AS REAL #Specific heat capacity of water


Cp_air AS REAL # Specific heat capacity of air

landa AS REAL #Heat of vaporisation

R AS REAL # Radius of the drum

VARIABLE

Omega AS no_unit # rotational speed

Tot_moist AS no_unit # moisture content balance

Tot_solid AS no_unit # Solid balance across unflighted section A

Tot_air AS no_unit # Gas balance across unflighted section A

k4_2 AS no_unit # Solid velocity



215

f AS no_unit ## area correction factor for section A

ha AS no_unit # area correction factor for section B

hb AS no_unit # area correction factor for section C

hc AS no_unit # area correction factor for section D

n AS no_unit ## area correction factor for section E

L AS no_unit # Length

f AS no_unit ## area correction factor for section A

y AS no_unit # axial dispersed coefficient

Energy_1 AS no_unit # Energy balance across unflighted section A

F_ain AS mass_flowrate # Gas flow rate

Tamb AS temperature # Ambient temperature

Energy AS no_unit # Energy balance across the dryer

lo_factor AS no_unit # Heat loss factor

Tot_solid_2 AS no_unit #Solid balance across flighted sections

Tot_air_2 AS no_unit #Gas balance across flighted sections

Energy_2 AS no_unit # Energy balance across flighted section

Energy_3 AS no_unit # Energy balance on unflighted section E

UNIT

C1 AS Kilning_Cell_1

C2 AS ARRAY(N2) OF Cell1



C5 AS Mixing

216

C6 AS Kilning_Cell_2

O AS Outflow

SET

C1.sl := [BFDM,2, 60];

C6.sl := [BFDM, 2, 100];

#C1.sl := [OCFEM,3, 30];

#C6.sl := [OCFEM, 3, 30];

EQUATION

L = L1 + L2 + L3 + L4 + L5;

#C1.U:= 0.161318 +(0.006533*omega) –(0.04198*(R*2));

k4_2=C1.u;

k4_3= C1.u;

k4_4= C1.u;

C6.u = C1.u;

# Area and heat loss factors

C1.f =f ; # factor

C1.lo = lo_factor;

C6.lo = lo_factor;

C6.n =n;

# axial dispersion coefficient

C1.k =y ; # axial dispersion coefficient

C6.k =y; # axial dispersion coefficient

C1.F_ain = F_ain;

217

C1.Tamb = Tamb;

C6.Tamb = Tamb;

# Section 2

FOR i:=1 TO N2-1 DO

C2(i).P.Kiln_out IS C2(i+1).P.Kiln_in;

C2(i).A.Axial IS C2(i+1).P.Axial;

C2(i).AIR.Air_out IS C2(i+1).AIR.Air_in;

END

C2(1).P.F_x = 0;

C2(1).P.T_x = 0;

C2(1).P.x_x = 0;

C2(1).P.tx = 0;

# Section 3

FOR i:=1 TO N3-1 DO




END

FOR i:=1 TO N4-1 DO




END

218

#Connecting Sections 1 and 2

C1.Kiln_out IS C2(1).P.Kiln_in;

C1.Air_out IS C2(1).AIR.Air_in;

# Connecting Sections 2 and 3

C2(N2).P.Kiln_out IS C3(1).P.Kiln_in;

C2(N2).A.Axial IS C3(1).P.Axial;

C2(N2).AIR.Air_out is C3(1).AIR.Air_in;

C3(N3).P.Kiln_out IS C4(1).P.Kiln_in;

C3(N3).A.Axial IS C4(1).P.Axial;

C3(N3).AIR.Air_out is C4(1).AIR.Air_in;

# Connecting Sections 3 and 4

C4(N4).P.Kiln_out IS C5.Passive;

C4(N4).A.Axial IS C5.Axial;

C5.out IS C6.Kiln_in;

C4(N4).AIR.Air_out is C6.Air_in;

# Setting Coefficients

FOR i:=1 TO N2 DO

C2(i).P.k_4 = k4_2/(L2/N2);

C2(i).A.h = ha;

C2(i).G.Phi = (419.6*C2(i).P.x_p)-7.801;

C2(i).AIR.lo= lo_factor;

C2(i).AIR.Ts =105 ;

C2(i).AIR.Tamb = Tamb;

219

C2(i).G.rhob = (-3095.24*C2(i).P.x_p)+ 2043.81;

C2(i).AIR.L = L2/N2 ;

C2(i).A.dp = 0.015;

C2(i).AIR.dp = 0.015;

C2(i).G.omega = omega;

END

FOR i:=1 TO N3 DO

C3(i).P.k_4 = k4_3/(L3/N3);

C3(i).AIR.dp = 0.012;

C3(i).A.dp = 0.012;

C3(i).A.h = hb;

C3(i).G.Phi = (419.6*C3(i).P.x_p)-7.801;


C3(i).AIR.Ts =100;


C3(i).AIR.L = L3/N3 ;

C3(i).G.rhob = (-3095.24*C3(i).P.x_p)+ 2043.81;


END

FOR i:=1 TO N4 DO

C4(i).P.k_4 = k4_4/(L4/N4);

C4(i).A.h = hc;

C4(i).G.Phi = (419.6*C4(i).P.x_p)-7.801;

220

C4(i).AIR.Ts =100 ;

C4(i).AIR.L = L4/N4 ;


C4(i).AIR.dp = 0.008;

C4(i).A.dp = 0.008;


C4(i).G.rhob = (-3095.24*C4(i).P.x_p)+ 2043.81;


END

O.Passive IS C6.Kiln_out;

O.Air_in IS C6.Air_out;

O.T_mass = 0.304; # This value must match the value of the tracer conc. in the Process entity.

#Overall Mass and energy balances

Tot_air = (C1.A_o*(1-C1.H_o))- ((C1.F_ain/3600)*(1-C1.H_ain));

Tot_air_2 = (C4(22).AIR.A_out*(1-C4(22).AIR.H_out))- ((C1.A_o)*(1-C1.H_o));

Tot_solid =C1.F_k_out*(1-C1.x_out) - C1.F_k_in*(1-C1.x_in);

Tot_moist =(C6.A_o*(C6.H_o)+ O.F_o*(O.x_o))-

(C1.F_k_in*(C1.x_in)+((C1.F_ain/3600)*(C1.H_ain)));

Tot_solid_2 =C5.F_t*(1-C5.x_t) - C1.F_k_out*(1-C1.x_out);

#Overall energy balance around the first unflighted section

Energy_1 = C1.F_k_out*(1-C1.x_out)*Cp_z*C1.Tout + C1.F_K_out*C1.x_out*Cp_w*C1.tout

+ C1.A_o*Cp_air*(1-C1.H_o)*100 + C1.A_o*Cp_w*C1.H_o*100 + C1.A_o*Cp_air*(1-

C1.H_o)*(C1.T_o-100) + C1.A_o*C1.Cpw_v(L1)*C1.H_o*(C1.T_o-100) +

221

C1.A_o*landa*C1.H_o- (C1.F_k_in*(1-C1.x_in)*Cp_z*C1.tink +

C1.F_k_in*C1.x_in*Cp_w*C1.tink + (C1.F_ain/3600)*Cp_air*(1-C1.H_ain)*(C1.T_airin-100)

+(C1.F_ain/3600)*C1.Cpw_v(0)*C1.H_ain*(C1.T_airin-100) + (C1.F_ain/3600)*Cp_air*(1-

C1.H_ain)*100 +(C1.F_ain/3600)*Cp_w*C1.H_ain*100 + (C1.F_ain/3600)*landa*C1.H_ain);

#Overall energy balance around flighted sections

Energy_2 = (C5.F_t*(1-C5.x_t)*Cp_z*C5.tt + C5.F_t*C5.x_t*Cp_w*C5.tt +

C4(22).AIR.A_out*Cp_air*(1-C4(22).AIR.H_out)*100 +

C4(22).AIR.A_out*Cp_w*C4(22).AIR.H_out*100 +

C4(22).AIR.A_out*landa*C4(22).AIR.H_out+ C4(22).AIR.A_out*Cp_air*(1-

C4(22).AIR.H_out)*(C4(22).AIR.T_airout -100) +

C4(22).AIR.A_out*C4(22).AIR.Cpw_v*C4(22).AIR.H_out*(C4(22).AIR.T_airout-100)) -

(C1.F_k_out*(1-C1.x_out)*Cp_z*C1.tout + C1.F_k_out*C1.x_out*Cp_w*C1.tout +

(C1.A_o)*Cp_air*(1-C1.H_o)*100 + C1.A_o*Cp_w*C1.H_o*100 + C1.A_o*landa*C1.H_o +

(C1.A_o)*Cp_air*(1-C1.H_o)*(C1.T_o-100) + C1.A_o*C1.Cpw_v(0)*C1.H_o*(C1.T_o-100));

#Overall energy balance around last unflighted section

Energy_3 = (O.F_o*(1-O.x_o)*Cp_z*O.tout + O.F_o*O.x_o*Cp_w*O.tout +

C6.A_o*Cp_air*(1-C6.H_o)*100 + C6.A_o*Cp_w*C6.H_o*100 + C6.A_o*landa*C6.H_o +

C6.A_o*Cp_air*(1-C6.H_o)*(C6.T_o-100) + C6.A_o*C6.Cpw_v(L5)*C6.H_o*(C6.T_o-100)) -

(C5.F_t*(1-C5.x_t)*Cp_z*C5.tt + C5.F_t*C5.x_t*Cp_w*C5.tt +

C6.A_air*C6.H_out(0)*100*Cp_w +C6.A_air*(1-C6.H_out(0))*100*Cp_air +

C6.A_air*landa*C6.H_out(0) + C6.A_air*C6.H_out(0)*(C6.tair(0)-100)*C6.Cpw_v(0)

+C6.A_air*(1-C6.H_out(0))*(C6.tair(0)-100)*Cp_air);

222

#Overall energy balance across the dryer

Energy = O.F_o*(1-O.x_o)*Cp_z*O.tout + O.F_o*O.x_o*Cp_w*O.tout + C6.A_o*Cp_air*(1-

C6.H_o)*100 + C6.A_o*Cp_w*C6.H_o*100 + C6.A_o*landa*C6.H_o +C6.A_o*Cp_air*(1-

C6.H_o)*(C6.T_o-100) + C6.A_o*C6.Cpw_v(L5)*C6.H_o*(C6.T_o-100)- C1.F_k_in*(1-

C1.x_in)*Cp_z*C1.tink - C1.F_k_in*C1.x_in*Cp_w*C1.tink - (C1.F_ain/3600)*Cp_air*(1-

C1.H_ain)*C1.T_airin -(C1.F_ain/3600)*Cp_w*C1.H_ain*C1.T_airin -

(C1.F_ain/3600)*landa*C1.H_ain;

223

Air phase

PARAMETER

landa AS REAL # Heat of vaporization

Cp_w AS REAL # specific heat capacity of water

Cp_air AS REAL # specific heat capacity of air

VARIABLE

Rw AS mass_flowrate # Evaporation

A_in AS mass_flowrate #Gas inlet mass flow rate

A_out AS mass_flowrate # Gas outlet mass flow rate

H_in AS mass_fraction # Gas inlet humidity

H_out AS mass_fraction # Gas outlet humidity

T_airout AS temperature # Gas outlet temperature

T_airin AS temperature # Gas inlet temperature

ta AS temperature # Moisture Content in Active Phase

Area AS no_unit # Area of solid in contact with gas

conv_a AS no_unit # convective heat transfer(active)

R AS no_unit # Total resistance

h_rad AS no_unit # radiation heat transfer coefficient

e AS no_unit # Surface emissivity

e_s AS no_unit # emissivity for solid

et AS no_unit #stefan boltmanz

Ts AS temperature # Shell temperature

Re_in AS no_unit # Inside Reynolds number

224

k_air AS no_unit # Thermal conductivity

mu_g AS no_unit # Viscosity of gas

mu_s AS no_unit # Viscosity @ d surface

Pr AS no_unit # Prandtl number

rho_g AS no_unit # Density of gas

v_g AS no_unit # Velocity of gas

Cpw_v AS no_unit # specific heat capacity of water vapour

hout AS no_unit # Outside Convective heat transfer coefficient

hinside AS no_unit # Inside Convective heat transfer coefficient

Q AS no_unit # Heat loss

Ra AS no_unit # Rayleigh number

conv_in AS no_unit # Inside convection

conv_out AS no_unit # Outside convection

L AS no_unit # Length of cell

D_out AS no_unit # Outside diameter

D_in AS no_unit # Inside diameter

Cond AS no_unit # Conduction

Rad AS no_unit # Radiation

g AS no_unit # Acceleration due to gravity

B AS no_unit # expansion coefficient

Tamb AS no_unit # Ambient temperature

v AS no_unit # kinematic viscosity

alpha AS no_unit #Thermal diffusivity

225

R_out AS no_unit # Outside radius

R_in AS no_unit # Inside radius

K_airo AS no_unit # Air thermal conductivity based on shell temperature

h_rad_w AS no_unit # radiation heat transfer coefficient internal

St AS no_unit # Staton number

dp AS no_unit # diffusivity

hc AS no_unit # diffusivity

k_s AS no_unit # diffusivity

rad_solid AS no_unit # Heat transferred to the solid via radiation

Rad_w AS no_unit # Radiation from gas to wall

lo AS no_unit # heat loss factor

STREAM

Air_in :A_in,H_in,T_airin AS AIRFLOW

Air_out :A_out,H_out,T_airout AS AIRFLOW

Evaporation :Rw,area, ta AS EVAPORATION

Convection :conv_a AS CONVECTION

masstransfer :mu_g,rho_g,st AS masstransfer

Radiation :rad_solid AS RADIATION

EQUATION

# Mass and energy balance

A_out = A_in + Rw;

A_out*H_out = A_in*H_in + Rw;

226

A_out*100*Cp_air*(1-H_out)+ A_out*100*Cp_w*(H_out) + A_out*H_out*landa +

A_out*(T_airout-100)*Cp_air*(1-H_out)+ A_out*(T_airout-100)*Cpw_v*(H_out) =

A_in*100*Cp_air*(1-H_in) + A_in*100*Cp_w*(H_in) + A_in*H_in*landa + A_in*(T_airin-

100)*Cp_air*(1-H_in) + A_in*(T_airin-100)*Cpw_v*(H_in)+ Rw*(landa + (Cp_w*Ta))-

conv_a- rad_solid-Q;

# Properties of air

Pr = 0.70752;

v_g = A_in/(rho_g*3.142*(1.95^2));

mu_s = -7.479E-12*(ts^2) + 3.746E-08*(ts) + 1.824E-05;

k_air = -1.249E-08*(t_airin^2) + 6.699E-05*(t_airin) + 2.541E-02;

rho_g = 6.417E-13*(t_airin^4) - 2.673E-09*(t_airin^3) + 4.129E-06*(t_airin^2) - 3.037E-

03*t_airin + 1.225E+00;

mu_g = -7.479E-12*(t_airin^2) + 3.746E-08*(t_airin) + 1.824E-05;

# specific heat capacity of water vapour

Cpw_v = -0.00000000031759*(t_airin +273)^3 + 0.00000091451537*(t_airin +273)^2 -

0.00014971847134*(t_airin +273) + 1.84044937134494;

#Estimation of convective heat transfer to solid

hc = (0.33*(((v_g*rho_g*dp)/mu_g)^0.6)*(k_air/dp));

St = hc/(cp_air*rho_g*v_g);

conv_a = hc*Area*(T_airout-Ta);

#Estimation of radiation heat transfer to solid

e_s = 0.9;

rad_solid = e_s*et*Area*(((T_airout+273)^4)-((Ta+273)^4));

227

#Heat loss calculation

# Radiation from the environment

h_rad = e*et*((Ts+273) + (Tamb+273))*(((Ts+273)^2) + ((Tamb+273)^2));

e = 0.79;

et = 5.67E-08;

Rad = h_rad*2*3.142*R_out*L;

#Radiation from gas to walls

h_rad_w = e*et*((T_airout+273) + (Ts+273))*(((T_airout+273)^2) + ((Ts+273)^2));

Rad_w = h_rad_w*2*3.142*R_out*L;

# Inside convection

R_in = 1.90;

D_in = R_in*2;

Re_in = (v_g*D_in*rho_g)/mu_g;

hinside =( k_air/D_in)*0.027*(Re_in^0.8)*(Pr^(1/3))*((mu_g/mu_s)^0.14);

conv_in = (hinside*2*3.142*r_in*L);

#Outside convection

g = 9.81;

B = 1/(t_airin+273);

alpha = 5.776E-11*((ts+273)^2) + 1.345E-07*(ts+273) - 2.466E-05;

v =7.451E-11*((ts+273)^2) + 5.671E-08*(ts+273) - 8.152E-06;

Ra = (g*B*(Ts-Tamb)*(D_out^3))/(v*alpha);

R_out = 1.95;

D_out = R_out*2;

228

K_airo= -1.249E-08*(Ts^2) + 6.699E-05*(Ts) + 2.541E-02;

hout = (k_airo/D_out)*((0.60+((0.387*(Ra^(1/6)))/((1+((0.559/Pr)^(9/16)))^(8/27))))^2);

conv_out = hout*2*3.142*R_out*L;

#Conduction

cond = (LOG(R_out/r_in))/(k_s*2*3.142*L);

k_s = 54-3.33E-02*Ts;

# Total resistance

R = (1/(conv_in + rad_w)) + cond + (1/(conv_out+ rad));

# Heat loss

Q = lo*((T_airout - Tamb)/R);

229

Active phase

PARAMETER

Cp_w AS REAL #Specific heat capacity of water

Cp_z AS REAL # specific heat capacity of zinc

landa AS REAL #heat of vaporisation

Cp_air AS REAL # specific heat of air


rho_p AS REAL # Particle density of zinc

VARIABLE

m_a AS mass # Active Mass

F_a AS mass_flowrate # Mass Flow from Passive Phase

F_r AS mass_flowrate # Mass Flow to Passive Phase

F_x AS mass_flowrate # Axial Mass Flow

T_a AS mass_fraction # Moisture Content in Active Phase

T_in AS mass_fraction # Moisture Content in Flow from Passive

c1 AS no_unit # Geometric Solids Advance w/o Drag

ft AS no_unit # falling time

x_a AS mass_fraction # Moisture Content in Active Phase

x_in AS mass_fraction # Moisture Content in Flow from Passive

ta AS temperature # Moisture Content in Active Phase

tin AS temperature # Moisture Content in Flow from Passive

Rw AS mass_flowrate # Evaporation rate

Area AS no_unit # Area in contact with gas

230

v_g AS no_unit # Velocity of air

dp AS no_unit # Particle size diameter

conv_a AS no_unit # Convective heat transfer

T_airout AS temperature # Gas temperature

A_o AS mass_flowrate # Air mass flow rate

H_out AS mass_fraction # Gas humidity

hm AS no_unit # Mass transfer coefficient

Pw_s AS no_unit # Partial pressure of solid

Pw_air AS no_unit # vapour partial pressure

St AS no_unit # Stanton number

h AS no_unit # Area correction factor

Sc AS no_unit #Schmitt number

Pr AS no_unit #Prandtl number

da AS no_unit # diffusivity

mu_g AS no_unit # viscosity of gas

rho_g AS no_unit # density of gas

rad_solid AS no_unit

STREAM

Axial :F_x,T_a,x_a,ta AS SOLIDFLOW

Return :F_r,T_a,x_a,ta AS SOLIDFLOW

Active :F_a,T_in,x_in,tin AS SOLIDFLOW

Data :ft,c1 AS DATAA

Convection :conv_a AS CONVECTION

231

Air :A_o,H_out,T_airout AS AIRFLOW

Evaporation :Rw,area, ta AS EVAPORATION

masstransfer :mu_g,rho_g,st AS masstransfer

Radiation : rad_solid AS RADIATION

EQUATION

# Mass & Energy balance

$m_a = F_a -F_r - F_x;

$(m_a*T_a) = (F_a*T_in) - (F_r + F_x)*T_a;

$(m_a*x_a) = (F_a*x_in) - (F_r + F_x)*x_a - Rw;

F_r + F_x = m_a / ft;

F_x = c1*m_a/ft;

$((m_a*(1-x_a)* Cp_z*ta) + (m_a*x_a*Cp_w*ta)) =

F_a*(((1-x_in)*Cp_z*tin) + (x_in*Cp_w*tin))- (F_r + F_x)*(((1-x_a)*Cp_z*ta) +

(x_a*Cp_w*ta))-Rw*(landa + (Cp_w*Ta)) + conv_a + rad_solid ;

# Gas velocity

v_g = A_o/(rho_g*3.142*(1.95^2));

# Area in contact with gas

area =h*m_a*(( 2*3.142*((0.5*dp)^2))/(4/3*3.142*((0.5*dp)^3)*rho_p));

# Evaporation rate

Rw= hm*(area)*(Pw_s-Pw_air);

Pw_s = exp(23.56143-(4030.182/(Ta+ 235)));

Pw_air= H_out*P*(26/18);

Sc = mu_g/(rho_g*da);

232

hm = (rho_g/Pw_air)*st*v_g*((Pr/Sc)^(2/3));

da = 2.65E-05;

Pr = 0.7;

233

Passive phase

PARAMETER

Cp_w AS REAL # specific heat capacity of water

Cp_z AS REAL # specific heat capacity of zinc

VARIABLE

m_p AS mass # Passive Mass

m_load AS mass # Loading Mass

k_2 AS no_unit # Passive to Active Transport Coefficient

k_4 AS no_unit # Kilning Transport Coefficient

F_x AS mass_flowrate # Axial flow rate into Passive Phase

F_a AS mass_flowrate # Passive to Active Mass Flow

F_r AS mass_flowrate # Active to Passive Mass Flow

F_k_in AS mass_flowrate # Kilning Mass Flow into Passive

F_k_out AS mass_flowrate # Kilning Mass Flow out of Passive

T_x AS mass_fraction # Tracer Content in Axial Flow

T_p AS mass_fraction # Tracer Content in Passive Cell

T_r AS mass_fraction # Tracer Content in Return Flow

T_k_in AS mass_fraction # Tracer Content of incoming Kilning Flow

x_x AS mass_fraction # Moisture Content in Axial Flow

x_p AS mass_fraction # Moisture Content in Passive Cell

x_r AS mass_fraction # Moisture Content in Return Flow

x_k_in AS mass_fraction # Moisture content of kilning flow

tx AS temperature # Temperature of Axial Flow

234

tp AS temperature #Temperature of Passive Cell

tr AS temperature # Temperature of Return Flow

tkin AS temperature # Temperature of kilning flow

STREAM

Axial :F_x,T_x,x_x,tx AS SOLIDFLOW

Active :F_a,T_p,x_p,tp AS SOLIDFLOW

Return :F_r,T_r,x_r,tr AS SOLIDFLOW

Kiln_in :F_k_in,T_k_in,x_k_in,tkin AS SOLIDFLOW

Kiln_out :F_k_out,T_p,x_p,tp AS SOLIDFLOW

DataOut :m_p AS DATAF

DataIn :k_2,m_load AS DATAP

EQUATION

# Mass and Energy balance

IF m_p < m_load THEN

$m_p = F_x + F_k_in + F_r - F_a - F_k_out;

$(m_p*T_p) = (F_x*T_x) + (F_k_in*T_k_in) + (F_r*T_r) - (F_a*T_p) - (F_k_out*T_p);

$(m_p*x_p) = (F_x*x_x) + (F_k_in*x_k_in) + (F_r*x_r) - (F_a*x_p) - (F_k_out*x_p);

F_k_out = k_4*m_p;

F_a = k_2 * m_p;

$((m_p*(1-x_p)* Cp_z*tp) + (m_p*x_p*Cp_w*tp)) =

F_x*(((1-x_x)*Cp_z*tx)+(x_x*Cp_w*tx)) + F_k_in*(((1-x_k_in)*Cp_z*tkin) + (x_k_in*

Cp_w*tkin)) + F_r*(((1-x_r)*Cp_z*tr) + (x_r*Cp_w*tr))- F_a*(((1-x_p)*Cp_z*tp) +

(x_p*Cp_w*tp)) - F_k_out*(((1-x_p)*Cp_z*tp) + (x_p*Cp_w*tp)) ;

235

ELSE

$m_p = F_x + F_k_in + F_r - F_a - F_k_out;

$(m_p*T_p) = (F_x*T_x) + (F_k_in*T_k_in) + (F_r*T_r) - (F_a*T_p) - (F_k_out*T_p);

$(m_p*x_p) = (F_x*x_x) + (F_k_in*x_k_in) + (F_r*x_r) - (F_a*x_p) - (F_k_out*x_p);

F_k_out = k_4 * m_p;

F_a = k_2 * m_load;

$((m_p*(1-x_p)* Cp_z*tp) + (m_p*x_p*Cp_w*tp)) =

F_x*(((1-x_x)*Cp_z*tx)+(x_x*Cp_w*tx)) + F_k_in*(((1-x_k_in)*Cp_z*tkin) + (x_k_in*

Cp_w*tkin)) + F_r*(((1-x_r)*Cp_z*tr) + (x_r*Cp_w*tr))- F_a*(((1-x_p)*Cp_z*tp) +

(x_p*Cp_w*tp)) - F_k_out*(((1-x_p)*Cp_z*tp) + (x_p*Cp_w*tp));

END

236

Kilning cell for section A

PARAMETER

L1 AS REAL # Length of plug flow section



rho_p AS REAL # particle density of zinc



DISTRIBUTION_DOMAIN

sl AS [0:L1]

VARIABLE

# Solid phase

r AS DISTRIBUTION(sl) OF density # mass distribution along reactor

rhob AS DISTRIBUTION(sl) OF no_unit # Bulk solid density

T AS DISTRIBUTION(sl) OF mass_fraction # Tracer fraction

Ts AS DISTRIBUTION(sl) OF temperature # Temperature fraction

me AS DISTRIBUTION(sl) OF mass_fraction # moisture content

Rw AS DISTRIBUTION(sl) OF mass_flowrate # Evaporation

Pw_s AS DISTRIBUTION(sl) OF no_unit # Partial pressure of solid

Pw_a AS DISTRIBUTION(sl) OF no_unit # Vapour partial pressure

Cpw_v AS DISTRIBUTION(sl) OF no_unit #specific heat capacity of water vapour

T_k_in AS mass_fraction # Tracer conc. in inflow

T_out AS mass_fraction # Tracer conc. in outflow

237

F_k_in AS mass_flowrate # Solid inlet mass flow rate(kg/s

F_k_out AS mass_flowrate # Solid outlet mass flow rate(kg/s

the AS mass_flowrate # kilning angle

u AS no_unit # velocity of material in # m s^-1

k AS no_unit # dispersion coefficient # m^2 s^-1

M_active AS mass # mass in contact with gas # kg

x_out AS mass_fraction # Moisture content of solid leaving the plug flow

x_in AS mass_fraction # Moisture content of solid entering the plug flow

tink AS temperature # Solid inlet temperature

Tout AS temperature # Solid temperature at the plug flow outlet

da AS no_unit # Diffusivity

e_s AS no_unit # Solid surface emissivity

f AS no_unit # area correction factor

dp AS no_unit # particle size

L AS no_unit # Length of chord based on kilning mass

A AS no_unit # Area in contact with gas

# Gas phase

Air AS DISTRIBUTION(sl) OF mass # mass of air

v_g AS DISTRIBUTION(sl) OF no_unit # Velocity of gas

tair AS DISTRIBUTION(sl) OF temperature # temperate of air

H_out AS DISTRIBUTION(sl) OF mass_fraction # Gas humidity

F_ain AS mass_flowrate # Ga inlet mass flow rate

H_ain AS mass_fraction # Gas inlet humidity

238

T_airin AS temperature # Gas inlet temperature

A_o AS mass_flowrate # Mass of gas @ outlet

H_o AS mass_fraction # Gas humidity @ outlet

T_o AS temperature # Gas temperature @ outlet

rho_g AS DISTRIBUTION(sl) OF no_unit # Density of gas

k_air AS DISTRIBUTION(sl) OF no_unit #Thermal conductivity of air

hc AS DISTRIBUTION(sl) OF no_unit # Convective heat transfer

mu_g AS DISTRIBUTION(sl) OF no_unit # Viscosity of air

Sc AS DISTRIBUTION(sl) OF no_unit # Schmidit

St AS DISTRIBUTION(sl) OF no_unit # Staton number

hm AS DISTRIBUTION(sl) OF no_unit # Mass transfer coefficient

Re AS DISTRIBUTION(sl) OF no_unit # Mass transfer coefficient

Qlos AS DISTRIBUTION(sl) OF no_unit # Heat loss

rad_solid AS DISTRIBUTION(sl) OF no_unit # Radiation from gas to solid

h_rad_w AS DISTRIBUTION(sl) OF no_unit # Radiative heat transfer

coefficient

rad_w AS DISTRIBUTION(sl) OF no_unit # Radiation from gas to wall

Res AS DISTRIBUTION(sl) OF no_unit # Resistance

conv_in AS DISTRIBUTION(sl) OF no_unit # Inside Convective heat transfer

hinside AS DISTRIBUTION(sl) OF no_unit #convective heat transfer

coefficient (from the gas to the wall)

Re_in AS DISTRIBUTION (sl) OF no_unit # Inside Reynolds number

conv_out AS no_unit # Outside convective heat transfer coefficient

239

hout AS no_unit # outside convection


Pr AS no_unit # Prandtl

cond AS no_unit # Conduction


g AS no_unit # acceleration due to gravity



v AS no_unit # Kinematic viscosity

alpha AS no_unit #Thermal expansion

h_rad AS no_unit # Radiation heat transfer coefficient

e AS no_unit # emissivity

et AS no_unit # Stefan-Boltzmann

lo AS no_unit # Heat loss factor

heatloss AS no_unit # Total heat lost

K_airo AS no_unit # thermal conductivity of air based on shell temperature

#Geometry



R_out AS no_unit # Inside radius #m

R_in AS no_unit # Outside radius

d AS no_unit # Discretised cell length

#Shell properties

240

Tsd AS temperature # Dryer shell temperature

mu_s AS no_unit # viscosity of gas @ shell temperature

k_s AS no_unit # thermal conductivity of steel material

STREAM

Kiln_in :F_k_in,T_k_in,x_in,tink AS SOLIDFLOW

Kiln_out :F_k_out,T_out, x_out,tout AS SOLIDFLOW

Air_out :A_o,H_o,T_o AS AIRFLOW

BOUNDARY

# Solid phase

r(0) = F_k_in/u;

T(0) = T_k_in;

me(0) = x_in;

Ts(0) = tink;

k*PARTIAL((Cp_w*Ts(L1)*r(L1)*me(L1)+ Cp_z*Ts(L1)*r(L1)*(1-me(L1))),sl,sl) = 0;

(k*(PARTIAL(r(L1),sl,sl))) = 0;

(k*(PARTIAL((r(L1)*T(L1)),sl,sl))) = 0;

(k*(PARTIAL((r(L1)*me(L1)),sl,sl))) = 0;

rhob(0) = (-3095.24*me(0))+ 2043.81;

rhob(L1) = (-3095.24*me(L1))+ 2043.81;

#Evaporation rate

Rw(0) = hm(0)*A*(Pw_s(0) - Pw_a(0));

Rw(L1) = hm(L1)*A*(Pw_s(L1) - Pw_a(L1));

hm(0) = (rho_g(0)/Pw_a(0))*st(0)*v_g(0)*((Pr/Sc(0))^(2/3));

241

hm(L1) = (rho_g(L1)/Pw_a(L1))*st(L1)*v_g(L1)*((Pr/Sc(L1))^(2/3));

Pw_s(0) = exp(23.56143-(4030.182/(Ts(0)+ 235)));

Pw_s(L1) = exp(23.56143-(4030.182/(Ts(L1)+ 235)));

Pw_a(0)= H_out(0)*101325*(26/18);

Pw_a(L1)= H_out(L1)*101325*(26/18);

# Gas phase

Tair(0) = T_airin;

PARTIAL((Air(L1)*(1-H_out(L1))*v_g(L1)*Cp_air*100 +

Air(L1)*H_out(L1)*Cp_w*v_g(L1)*100 + Air(L1)*(1-H_out(L1))*v_g(L1)*Cp_air*(tair(L1)-

100) + Air(L1)*H_out(L1)*Cpw_v(L1)*v_g(L1)*(tair(L1)-100)+

Air(L1)*H_out(L1)*v_g(L1)*landa) ,sl)= 0

H_out(0) = H_ain;

(PARTIAL((Air(L1)*H_out(L1)*v_g(L1)),sl)) = 0;

Air(0) = (F_ain/3600)/v_g(0);

(PARTIAL(Air(L1)*v_g(L1),sl)) = 0;

#Gas properties

rho_g(0) = 6.417E-13*(tair(0)^4) - 2.673E-09*(tair(0)^3) + 4.129E-06*(tair(0)^2) - 3.037E-

03*tair(0) + 1.225E+00;

k_air(0) = -1.249E-08*(tair(0)^2) + 6.699E-05*(tair(0)) + 2.541E-02;

mu_g(0) = -7.479E-12*(tair(0)^2) + 3.746E-08*(tair(0)) + 1.824E-05;

rho_g(L1) = 6.417E-13*(tair(L1)^4) - 2.673E-09*(tair(L1)^3) + 4.129E-06*(tair(L1)^2) -

3.037E-03*tair(L1) + 1.225E+00;

k_air(L1) = -1.249E-08*(tair(L1)^2) + 6.699E-05*(tair(L1)) + 2.541E-02;

242

mu_g(L1) = -7.479E-12*(tair(L1)^2) + 3.746E-08*(tair(L1)) + 1.824E-05;

St(0) = hc(0)/(Cp_air*rho_g(0)*v_g(0));

Sc(0) = mu_g(0)/(rho_g(0)*da);

St(L1) = hc(L1)/(Cp_air*rho_g(L1)*v_g(L1));

Sc(L1) = mu_g(L1)/(rho_g(L1)*da);

hc(0) = (0.33*(((v_g(0)*rho_g(0)*dp)/mu_g(0))^0.6)*(k_air(0)/dp));

hc(L1) = (0.33*(((v_g(L1)*rho_g(L1)*dp)/mu_g(L1))^0.6)*(k_air(L1)/dp));

Re(0) = (v_g(0)*dp*rho_g(0))/mu_g(0);

Re(L1) = (v_g(L1)*dp*rho_g(L1))/mu_g(L1);

v_g(0) = (F_ain/3600)/(rho_g(0)*3.142*(1.95^2));

v_g(L1) = (F_ain/3600)/(rho_g(L1)*3.142*(1.95^2));

Cpw_v(0) =-0.00000000031759*(tair(0)+273)^3 + 0.00000091451537*(tair(0)+273)^2 -

0.00014971847134*(tair(0)+273) + 1.84044937134494;

Cpw_v(L1) =-0.00000000031759*(tair(L1)+273)^3 + 0.00000091451537*(tair(L1)+273)^2 -

0.00014971847134*(tair(L1)+273) + 1.84044937134494;

#heat loss

Qlos(0) = lo*((tair(0) - Tamb)/Res(0));

Qlos(L1) = lo*((tair(L1) - Tamb)/Res(L1));

Res(0) = (1/(conv_in(0) + rad_w(0))) + cond +(1/(conv_out + rad));

Res(L1) = (1/(conv_in(L1) + rad_w(L1))) + cond +(1/(conv_out + rad));

rad_solid(0) = e_s*et*A*(((Tair(0)+273)^4)-((Ts(0)+273)^4));

rad_solid(L1) = e_s*et*A*(((Tair(L1)+273)^4)-((Ts(L1)+273)^4));

h_rad_w(0) = e*et*((Tair(0)+273) + (Tsd+273))*(((Tair(0)+273)^2) + ((Tsd+273)^2));

243

h_rad_w(L1) = e*et*((Tair(L1)+273) + (Tsd+273))*(((Tair(L1)+273)^2) + ((Tsd+273)^2));

Rad_w(0) = h_rad_w(0)*2*3.142*R_out;

Rad_w(L1) = h_rad_w(L1)*2*3.142*R_out;

Re_in(0) = (v_g(0)*D_in*rho_g(0))/mu_g(0);

hinside(0) =( k_air(0)/D_in)*0.027*(Re_in(0)^0.8)*(Pr^(1/3))*((mu_g(0)/mu_s)^0.14);

conv_in(0) = (hinside(0)*2*3.142*r_in);

Re_in(L1) = (v_g(L1)*D_in*rho_g(L1))/mu_g(L1);

hinside(L1) =( k_air(L1)/D_in)*0.027*(Re_in(L1)^0.8)*(Pr^(1/3))*((mu_g(L1)/mu_s)^0.14);

conv_in(L1) = (hinside(L1)*2*3.142*r_in);

EQUATION

# Area in contact with the gas

r(L1) =((1.95^2)/2)*rhob(0)*(the -Sin(the));

L = 2*1.95*Sin(the/2);

M_active = ((L*dp)/(((1.95^2)/2)*(the-Sin(the))))*r(L1)*d;

A =f*M_active*(( 2*3.142*((0.5*dp)^2))/(4/3*3.142*((0.5*dp)^3)*rho_p));

d =L1/60;

dp = 0.02;

da = 2.65E-05;

Pr = 0.7;

e_s = 0.9;

# Heat loss calculation

Tsd = 145;

# Radiation

244

h_rad = e*et*((Tsd+273) + (Tamb+273))*(((Tsd+273)^2) + ((Tamb+273)^2));

e = 0.79;

et = 5.67E-08;

Rad = h_rad*2*3.142*R_out;

# Inside convection

mu_s = 2.3650E-05;

R_in = 1.90;

D_in = R_in*2;

# Outside convection

g = 9.81;

B = 1.3E-03;

alpha =4.16531E-05;

v =2.8571E-05;

Ra = (g*B*(Tsd-Tamb)*(D_out^3))/(v*alpha);

R_out = 1.95;

D_out = R_out*2;

k_airo = 0.0348756;

hout = (k_airo/D_out)*((0.60+((0.387*(Ra^(1/6)))/((1+((0.559/Pr)^(9/16)))^(8/27))))^2);#W

m^-2 C^-1

conv_out = hout*2*3.142*R_out; #W m^-1 C^-1

# Conduction

k_s = 54-3.33E-02*Tsd; # W m^2 C^-1

#k_s =0.0348756;

245

cond = (LOG(R_out/r_in))/(k_s*2*3.142);

# Mass and Energy balance

FOR i:=0|+ TO L1|- DO

# Solid phase

$r(i) = (k*(PARTIAL(r(i),sl,sl)))-(u*(PARTIAL(r(i),sl))); # Solid mass (kg s^-1 m^-1)

# Tracer concentration

$(T(i)*r(i)) = (k*(PARTIAL((r(i)*T(i)),sl,sl)))-(u*(PARTIAL((r(i)*T(i)),sl)));

# Solid moisture content (kg s^-1 m^-1)

$(me(i)*r(i)) = (k*(PARTIAL((r(i)*me(i)),sl,sl)))-(u*(PARTIAL((r(i)*me(i)),sl)))-Rw(i)/d; #

Solid moisture content(kg s^-1 m^-1)

rhob(i) = (-3095.24*me(i))+ 2043.81; # Solid bulk denisty # kg m^3

# Solid temperature (J s^-1 m^-1)

$((Ts(i)*r(i)*Cp_w*me(i)) + (Ts(i)*r(i)*Cp_z*(1-me(i)))) =

k*PARTIAL((Cp_w*Ts(i)*r(i)*me(i)+ Cp_z*Ts(i)*r(i)*(1-me(i))),sl,sl)-

u*(PARTIAL((Cp_w*me(i)*Ts(i)*r(i)+ Cp_z*(1-me(i))*Ts(i)*r(i)),sl))- (Rw(i)/d)*(landa +

Cp_w*Ts(i)) + hc(i)*(A/d)*(tair(i)-Ts(i))+ (rad_solid(i)/d);

# Evaporation rate

Rw(i) = hm(i)*(A)*(Pw_s(i) - Pw_a(i));

hm(i) = (rho_g(i)/Pw_a(i))*st(i)*v_g(i)*((Pr/Sc(i))^(2/3));

Pw_s(i) = exp(23.56143-(4030.182/(Ts(i)+ 235)));

Pw_a(i)= H_out(i)*101325*(26/18);

# Air phase

$Air(i) = -PARTIAL((Air(i)*v_g(i)),sl) + Rw(i)/d;

246

$(Air(i)*H_out(i))= -PARTIAL((Air(i)*H_out(i)*v_g(i)),sl)+ Rw(i)/d;

#Gas temperature (J s^-1 m^-1)

$(Air(i)*(1-H_out(i))*v_g(i)*Cp_air*100 + Air(i)*H_out(i)*Cp_w*v_g(i)*100 + Air(i)*(1-

H_out(i))*v_g(i)*Cp_air*(tair(i)-100) + Air(i)*H_out(i)*Cpw_v(i)*v_g(i)*(tair(i)-100)+

Air(i)*H_out(i)*landa-(8.314*(Tair(i)+273)*(10^3)*(Air(i)*H_out(i)/18))-

(8.314*(10^3)*(Tair(i)+273)*(Air(i)*(1-H_out(i))/29))) = -PARTIAL((Air(i)*(1-

H_out(i))*v_g(i)*Cp_air*100 + Air(i)*H_out(i)*Cp_w*v_g(i)*100 + Air(i)*(1-


Air(i)*H_out(i)*v_g(i)*landa) ,sl) + (Rw(i)/d)*(landa + Cp_w*Ts(i))-hc(i)*(A/d)*(tair(i)-Ts(i))-

(rad_solid(i)/d)- Qlos(i) ;

#Gas properties

v_g(i) = (F_ain/3600)/(rho_g(i)*3.142*(1.95^2));

rho_g(i) = 6.417E-13*(tair(i)^4) - 2.673E-09*(tair(i)^3) + 4.129E-06*(tair(i)^2) - 3.037E-

03*tair(i) + 1.225E+00;

k_air(i) = -1.249E-08*(tair(i)^2) + 6.699E-05*(tair(i)) + 2.541E-02;

mu_g(i) = -7.479E-12*(tair(i)^2) + 3.746E-08*(tair(i)) + 1.824E-05;

St(i) = hc(i)/(Cp_air*rho_g(i)*v_g(i));

Sc(i) = mu_g(i)/(rho_g(i)*da);

hc(i) = (0.33*(((v_g(i)*rho_g(i)*dp)/mu_g(i))^0.6)*(k_air(i)/dp));

Re(i) = (v_g(i)*dp*rho_g(i))/mu_g(i);


Cpw_v(i) =-0.00000000031759*(tair(i)+273)^3 + 0.00000091451537*(tair(i)+273)^2 -

0.00014971847134*(tair(i)+273) + 1.84044937134494;

247

# Heat loss

Qlos(i) = lo*((tair(i) - Tamb)/Res(i));

# radiation from gas to solid

rad_solid(i) = e_s*et*A*(((Tair(i)+273)^4)-((Ts(i)+273)^4));

# radiation from gas to the wall

h_rad_w(i) = e*et*((Tair(i)+273) + (Tsd+273))*(((Tair(i)+273)^2) + ((Tsd+273)^2));

Rad_w(i) = h_rad_w(i)*2*3.142*R_out;

#Inside convective heat transfer (from gas to wall)

Re_in(i) = (v_g(i)*D_in*rho_g(i))/mu_g(i);

hinside(i) =( k_air(i)/D_in)*0.027*(Re_in(i)^0.8)*(Pr^(1/3))*((mu_g(i)/mu_s)^0.14);

conv_in(i) = (hinside(i)*2*3.142*r_in);

Res(i) = (1/(conv_in(i) + rad_w(i))) + cond +(1/(conv_out + rad));

END

#Total heat loss from the section

heatloss = INTEGRAL(i := 0:L1; Qlos(i));

# Variables linking the next section

r(L1) = F_k_out/u;

T(L1) = T_out;

me(L1) = x_out;

Ts(L1) = Tout;

Air(L1) = A_o/v_g(L1);

Tair(L1) = T_o;

H_out(L1) = H_o;

248

Kilning cell for section E

PARAMETER

L5 AS REAL # Length of plug flow section






rho_p AS REAL # Particle density of zinc

DISTRIBUTION_DOMAIN

sl AS [0:L5]

VARIABLE

# Solid phase

r AS DISTRIBUTION(sl) OF density # mass distribution along reactor

T AS DISTRIBUTION (sl) OF mass_fraction # Tracer fraction

Ts AS DISTRIBUTION (sl) OF temperature # Temperature

me AS DISTRIBUTION(sl) OF mass_fraction # moisture content

Rw AS DISTRIBUTION(sl) OF mass_flowrate # Evaporation

Pw_s AS DISTRIBUTION(sl) OF no_unit # Partial pressure of solid

Pw_a AS DISTRIBUTION(sl) OF no_unit # Vapour partial pressure

rhob AS DISTRIBUTION(sl) OF no_unit # Density of solid

Cpw_v AS DISTRIBUTION(sl) OF no_unit #specific heat capacity of water vapour

249

F_t AS mass_flowrate # mass flow rate into the section

T_t AS mass_fraction # tracer fraction entering the section

x_t AS mass_fraction # moisture content entering the section

tt AS temperature # Solid temperature(inlet)

da AS no_unit # Diffusivity

Tout AS temperature # Solid temperature at the plug flow outlet

T_out AS mass_fraction # Tracer conc. in outflow

F_k_out AS mass_flowrate # Mass flow out

the AS mass_flowrate # kilning angle

u AS no_unit # solid velocity

k AS no_unit # dispersion coefficient

M_active AS mass # mass in contact with gas

x_out AS mass_fraction # Moisture content of solid leaving plug flow

dp AS no_unit # particle size

e_s AS no_unit # Solid surface emissivity

L AS no_unit # Length of chord

A AS no_unit # Area in contact with gas

n AS no_unit # Area correction factor

# Gas Phase

Air AS DISTRIBUTION(sl) OF mass # mass of air

v_g AS DISTRIBUTION(sl) OF no_unit

Qlos AS DISTRIBUTION(sl) OF no_unit # Heat loss

250

tair AS DISTRIBUTION(sl) OF temperature # temperate of air

rho_g AS DISTRIBUTION(sl) OF no_unit #density of gas

k_air AS DISTRIBUTION(sl) OF no_unit # thermal conductivity of air

hc AS DISTRIBUTION(sl) OF no_unit #Convective heat transfer

coefficient(from gas to solids)

mu_g AS DISTRIBUTION(sl) OF no_unit # Viscosity of air

Sc AS DISTRIBUTION(sl) OF no_unit # Schmidt

St AS DISTRIBUTION (sl) OF no_unit # Stanton number

hm AS DISTRIBUTION(sl) OF no_unit # Mass transfer coefficient

H_out AS DISTRIBUTION (sl) OF mass_fraction # Gas humidity

rad_solid AS DISTRIBUTION(sl) OF no_unit # Mass transfer coefficient

h_rad_w AS DISTRIBUTION(sl) OF no_unit # Heat loss

rad_w AS DISTRIBUTION(sl) OF no_unit # Heat loss

Res AS DISTRIBUTION(sl) OF no_unit # Heat loss

Re_in AS DISTRIBUTION(sl) OF no_unit # Inside Reynolds number

hinside AS DISTRIBUTION(sl) OF no_unit # Inside convection transfer

coefficient(from gas to walls)

conv_in AS DISTRIBUTION(sl) OF no_unit # inside convective heat

transfer(from gas to walls)

A_o AS mass_flowrate # Gas mass flow rate at outlet

H_o AS mass_fraction # Gas humidity at outlet

T_o AS temperature # Gas temperature at outlet

Pr AS no_unit # Prandtl number

251

hout AS no_unit # outside convection


conv_out AS no_unit # Outside convective heat transfer coefficient

Cond AS no_unit # Conduction


g AS no_unit # acceleration due to gravity



v AS no_unit # Kinematic viscosity

alpha AS no_unit

h_rad AS no_unit # Radiation heat transfer coefficient

e AS no_unit # emissivity

et AS no_unit # Stefan-Boltzmann

A_air AS mass_flowrate # Gas mass flow rate

H_t AS mass_fraction # Gas humidity at inlet

T_air AS temperature # Gas temperature at inlet

lo AS no_unit # heat loss correction factor

heatloss AS no_unit # Total heat loss

#Shell properties

mu_s AS no_unit # viscosity of gas @ shell temperature

K_airo AS no_unit # Therrmal conductivity of air based on shell temperature

k_s AS no_unit # Thermal conductivity of shell

Tsd AS temperature # Dryer shell temperature

252

#Geometry



R_out AS no_unit # Inside radius

R_in AS no_unit # Outside radius

d AS no_unit # Discertized cell length

STREAM

Kiln_in :F_t, T_t, x_t, tt AS SOLIDFLOW

Kiln_out :F_k_out,T_out,x_out,tout AS SOLIDFLOW

Air_in :A_air,H_t,T_air AS AIRFLOW

Air_out : A_o, H_o, T_o AS AIRFLOW

BOUNDARY

r(0) = (F_t)/u;

T(0) = T_t ;

Ts(0) = tt ;

me(0) = x_t ;

(k*(PARTIAL(r(L5),sl,sl))) = 0;

(k*(PARTIAL((r(L5)*T(L5)),sl,sl))) = 0;

(k*(PARTIAL((r(L5)*me(L5)),sl,sl))) = 0;

(k*(PARTIAL((Cp_w*Ts(L5)*r(L5)*me(L5)+ Cp_z*Ts(L5)*r(L5)*(1-me(L5))),sl,sl))) = 0;

Air(0) = A_air/v_g(0);

(PARTIAL(Air(L5)*v_g(L5),sl)) = 0;

253

Tair(0) = T_air;

PARTIAL((Air(L5)*(1-H_out(L5))*v_g(L5)*Cp_air*100 +

Air(L5)*H_out(L5)*Cp_w*v_g(L5)*100 + Air(L5)*(1-H_out(L5))*v_g(L5)*Cp_air*(tair(L5)-

100) + Air(L5)*H_out(L5)*Cpw_v(L5)*v_g(L5)*(tair(L5)-100)+

Air(L5)*H_out(L5)*v_g(L5)*landa) ,sl)= 0;

H_out(0) = H_t;

(PARTIAL((Air(L5)*H_out(L5)*v_g(L5)),sl)) = 0;

Rw(0) = hm(0)*A*(Pw_s(0) - Pw_a(0));

Rw(L5) = hm(L5)*A*(Pw_s(L5) - Pw_a(L5));

Pw_s(0) = exp(23.56143-(4030.182/(Ts(0)+ 235)));

Pw_s(L5) = exp(23.56143-(4030.182/(Ts(L5)+ 235)));

Pw_a(0)= H_out(0)*P*(26/18);

Pw_a(L5)= H_out(L5)*P*(26/18);

Qlos(0) = lo*((tair(0) - Tamb)/Res(0));

Qlos(L5) =lo*((tair(L5) - Tamb)/Res(L5));

rho_g(0) = 6.417E-13*(tair(0)^4) - 2.673E-09*(tair(0)^3) + 4.129E-06*(tair(0)^2) - 3.037E-

03*tair(0) + 1.225E+00;

rho_g(L5) = 6.417E-13*(tair(L5)^4) - 2.673E-09*(tair(L5)^3) + 4.129E-06*(tair(L5)^2) -

3.037E-03*tair(L5) + 1.225E+00;

k_air(0) = -1.249E-08*(tair(0)^2) + 6.699E-05*(tair(0)) + 2.541E-02;

k_air(L5) = -1.249E-08*(tair(L5)^2) + 6.699E-05*(tair(L5)) + 2.541E-02;

mu_g(0) = -7.479E-12*(tair(0)^2) + 3.746E-08*(tair(0)) + 1.824E-05;

mu_g(L5) = -7.479E-12*(tair(L5)^2) + 3.746E-08*(tair(L5)) + 1.824E-05;

254

Cpw_v(0) =-0.00000000031759*(tair(0)+273)^3 + 0.00000091451537*(tair(0)+273)^2 -

0.00014971847134*(tair(0)+273) + 1.84044937134494;

Cpw_v(L5) =-0.00000000031759*(tair(L5)+273)^3 + 0.00000091451537*(tair(L5)+273)^2 -

0.00014971847134*(tair(L5)+273) + 1.84044937134494;

St(0) = hc(0)/(Cp_air*rho_g(0)*v_g(0));

St(L5) = hc(L5)/(Cp_air*rho_g(L5)*v_g(L5));

Sc(0) = mu_g(0)/(rho_g(0)*da);

Sc(L5) = mu_g(L5)/(rho_g(L5)*da);

hm(0) = (rho_g(0)/Pw_a(0))*st(0)*v_g(0)*((Pr/Sc(0))^(2/3));

hm(L5) = (rho_g(L5)/Pw_a(L5))*st(L5)*v_g(l5)*((Pr/Sc(L5))^(2/3));

hc(0) = (0.33*(((v_g(0)*rho_g(0)*dp)/mu_g(0))^0.6)*(k_air(0)/dp));

hc(L5) = (0.33*(((v_g(L5)*rho_g(L5)*dp)/mu_g(L5))^0.6)*(k_air(L5)/dp));

rhob(0) = (-3095.24*me(0))+ 2043.81; # Angle of repose

rhob(L5) = (-3095.24*me(L5))+ 2043.81; # Angle of repose

rad_solid(0) = e_s*et*A*(((Tair(0)+273)^4)-((Ts(0)+273)^4));

rad_solid(L5) = e_s*et*A*(((Tair(L5)+273)^4)-((Ts(L5)+273)^4));

h_rad_w(0) = e*et*((Tair(0)+273) + (Tsd+273))*(((Tair(0)+273)^2) + ((Tsd+273)^2));

h_rad_w(L5) = e*et*((Tair(L5)+273) + (Tsd+273))*(((Tair(L5)+273)^2) + ((Tsd+273)^2));

Res(0) = (1/(conv_in(0) + rad_w(0))) + cond +(1/(conv_out + rad));

Res(L5) = (1/(conv_in(L5) + rad_w(L5))) + cond +(1/(conv_out + rad));

Rad_w(0) = h_rad_w(0)*2*3.142*R_out;

Rad_w(L5) = h_rad_w(L5)*2*3.142*R_out;

Re_in(0) = (v_g(0)*D_in*rho_g(0))/mu_g(0);

255

Re_in(L5) = (v_g(L5)*D_in*rho_g(L5))/mu_g(L5);

hinside(0) =( k_air(0)/D_in)*0.027*(Re_in(0)^0.8)*(Pr^(1/3))*((mu_g(0)/mu_s)^0.14);

hinside(L5) =( k_air(L5)/D_in)*0.027*(Re_in(L5)^0.8)*(Pr^(1/3))*((mu_g(L5)/mu_s)^0.14);

conv_in(0) = (hinside(0)*2*3.142*r_in);

conv_in(L5) = (hinside(L5)*2*3.142*r_in);

v_g(0) = A_air/(rho_g(0)*3.142*(1.95^2));

v_g(L5) = A_air/(rho_g(L5)*3.142*(1.95^2));

EQUATION

# Area in contact with the gas

r(L5) =((1.95^2)/2)*rhob(0)*(the -Sin(the)); # Area of kilning

L = 2*1.95*Sin(the/2); # length of chord

M_active = ((L*dp)/(((1.95^2)/2)*(the-Sin(the))))*r(L5)*d;

A =n*M_active*(( 2*3.142*((0.5*dp)^2))/(4/3*3.142*((0.5*dp)^3)*rho_p));

d =L5/100;

dp = 0.007;

da = 2.65E-05;

Pr = 0.7;

e_s = 0.9;

#Heat loss calculation

Tsd = 65;

# Radiation heat transfer to the environment

h_rad = e*et*((Tsd+273) + (Tamb+273))*(((Tsd+273)^2) + ((Tamb+273)^2));

e = 0.79;

256

et = 5.67E-08;

Rad = h_rad*2*3.142*R_out;

# Inside convection heat transfer from gas to walls

R_in = 1.90;

D_in = R_in*2;

mu_s = 2.3E-05;

# Outside convection heat transfer from walls to environment

R_out = 1.95;

D_out = R_out*2;

g = 9.81; # acceleration

B = 1/(tair(0)+273);

alpha = 2.7399E-05;

v =2.0366E-05;

Ra = (g*B*(Tsd-Tamb)*(D_out^3))/(v*alpha);

k_airo = 0.029668371;

hout = (k_airo/D_out)*((0.60+((0.387*(Ra^(1/6)))/((1+((0.559/Pr)^(9/16)))^(8/27))))^2);

conv_out = hout*2*3.142*R_out;

# Conduction

k_s = 54-3.33E-02*Tsd;

cond = (LOG(R_out/r_in))/(k_s*2*3.142);

# Mass and energy balance

FOR i: =0|+ TO L5|- DO

# Solid phase

257

$r(i) = (k*(PARTIAL(r(i),sl,sl)))-(u*(PARTIAL(r(i),sl)));

$(T(i)*r(i)) = (k*(PARTIAL((r(i)*T(i)),sl,sl)))-(u*(PARTIAL((r(i)*T(i)),sl)));

$(me(i)*r(i)) = (k*(PARTIAL((r(i)*me(i)),sl,sl)))-(u*(PARTIAL((r(i)*me(i)),sl)))-Rw(i)/d;

$((Ts(i)*r(i)*Cp_w*me(i)) + (Ts(i)*r(i)*Cp_z*(1-me(i)))) =

k*PARTIAL((Cp_w*Ts(i)*r(i)*me(i)+ Cp_z*Ts(i)*r(i)*(1-me(i))),sl,sl)-

u*(PARTIAL((Cp_w*me(i)*Ts(i)*r(i)+ Cp_z*(1-me(i))*Ts(i)*r(i)),sl))- (Rw(i)/d)*(landa +

Cp_w*Ts(i)) + hc(i)*(A/d)*(tair(i)-Ts(i)) + (rad_solid(i)/d);

rhob(i) = (-3095.24*me(i))+ 2043.81;

Rw(i) = hm(i)*(A)*(Pw_s(i) - Pw_a(i));

Pw_s(i) = exp(23.56143-(4030.182/(Ts(i)+ 235)));

Pw_a(i)= H_out(i)*P*(26/18);

# Air phase

$(Air(i)*(1-H_out(i))*v_g(i)*Cp_air*100 + Air(i)*H_out(i)*Cp_w*v_g(i)*100 + Air(i)*(1-


Air(i)*H_out(i)*landa-(8.314*(Tair(i)+273)*(10^3)*(Air(i)*H_out(i)/18))-

(8.314*(10^3)*(Tair(i)+273)*(Air(i)*(1-H_out(i))/29))) = -PARTIAL((Air(i)*(1-

H_out(i))*v_g(i)*Cp_air*100 + Air(i)*H_out(i)*Cp_w*v_g(i)*100 + Air(i)*(1-


Air(i)*H_out(i)*v_g(i)*landa) ,sl) + (Rw(i)/d)*(landa + Cp_w*Ts(i))-hc(i)*(A/d)*(tair(i)-Ts(i))-

(rad_solid(i)/d)- Qlos(i) ;

v_g(i) = A_air/(rho_g(i)*3.142*(1.95^2));

Qlos(i) = lo*((tair(i) - Tamb)/Res(i)); # Heat loss

258

rho_g(i) = 6.417E-13*(tair(i)^4) - 2.673E-09*(tair(i)^3) + 4.129E-06*(tair(i)^2) - 3.037E-

03*tair(i) + 1.225E+00;

k_air(i) = -1.249E-08*(tair(i)^2) + 6.699E-05*(tair(i)) + 2.541E-02;

mu_g(i) = -7.479E-12*(tair(i)^2) + 3.746E-08*(tair(i)) + 1.824E-05;

St(i) = hc(i)/(Cp_air*rho_g(i)*v_g(i));

Sc(i) = mu_g(i)/(rho_g(i)*da);

hm(i) = (rho_g(i)/Pw_a(i))*st(i)*v_g(i)*((Pr/Sc(i))^(2/3));

hc(i) = (0.33*(((v_g(i)*rho_g(i)*dp)/mu_g(i))^0.6)*(k_air(i)/dp));

rad_solid(i) = e_s*et*A*(((Tair(i)+273)^4)-((Ts(i)+273)^4));

h_rad_w(i) = e*et*((Tair(i)+273) + (Tsd+273))*(((Tair(i)+273)^2) + ((Tsd+273)^2));

Rad_w(i) = h_rad_w(i)*2*3.142*R_out;

Re_in(i) = (v_g(i)*D_in*rho_g(i))/mu_g(i);

hinside(i) =( k_air(i)/D_in)*0.027*(Re_in(i)^0.8)*(Pr^(1/3))*((mu_g(i)/mu_s)^0.14);

conv_in(i) = (hinside(i)*2*3.142*r_in);

Res(i) = (1/(conv_in(i) + rad_w(i))) + cond +(1/(conv_out + rad));


Cpw_v(i) =-0.00000000031759*(tair(i)+273)^3 + 0.00000091451537*(tair(i)+273)^2 -

0.00014971847134*(tair(i)+273) + 1.84044937134494;

END

#Total heat loss from this section

heatloss = INTEGRAL(i := 0:L5; Qlos(i));

# Outlet variables

r(L5) = F_k_out/u;

259

T(L5) = T_out;

me(L5) = x_out;

Ts(L5) = Tout;

Air(L5) = A_o/v_g(L5);

Tair(L5) = T_o;

H_out(L5) = H_o;

260

Geometric modelling for section B

PARAMETER

L2 AS REAL # Drum Length (m)






alpha1_2 AS REAL # Flight Angle 1 (deg)


N2 AS INTEGER # Number of Cells

VARIABLE

omega AS no_unit # Angular Velocity of Drum (RPM)

m_p AS mass # Passive Mass from Passive Phase

m_load AS mass # Calculated Loging Mass for Passive Phase

load AS no_unit # Loading Level of Flight

U AS no_unit # Unloading Level of Flight

phi AS no_unit # Angle of Repose of Solids in Flights

a1 AS no_unit # alpha1 in radians


Rf AS length # Radius of flight tip

psi_ft AS no_unit # Angle between flight tip and flight base from centre of

dryer

261

c1 AS no_unit # Geometricaly Calculated Axial Advance

k_2 AS no_unit

maft AS no_unit # Mass averaged fall time of solids

mafh AS length # Mass averaged fall height of solids

tpas AS no_unit # Average passive cycle time

dl AS length # Length of cell

pi AS no_unit # Pi

#sf AS no_unit # Scaling factor

m_bak AS mass # Design load

m_des AS mass # modified design load

rhob AS no_unit # Density of Solids

STREAM

Data_In :m_p AS DATAF

Data_A :maft,c1 AS DATAA

Data_P :k_2,m_load AS DATAP

EQUATION

pi = 3.141592654;

dl = L2/N2; # Length of Slice

a1 = alpha1_2*pi/180; # Convert alpha1 to radians


# Basic Dryer Geometry Calculations

# Calculation of flight tip radius

Rf = sqrt(((R-s1_2)^2) + (s2_2^2) - 2*s2_2*(R-s1_2)*cos((3/2)*pi-a1-a2));

262

# Calculation of angle between flight tip and flight base from centre of dryer

psi_ft = asin(s2_2*sin(pi-a2)/Rf);

# Calculating Theoretical Loading Mass using Porter's Assumption

m_bak = rhob*dl*(-8.44885457098519+ 1.20811962158233*phi -0.0696338151338383*(phi^2)

+ 0.00212647019010012*(phi^3) -3.60759970976406E-05*(phi^4) + 3.22758303782236E-

07*(phi^5)-1.18976131428293E-09*(phi^6));

m_des = (1.24*m_bak);

m_load = m_des;

# Calculating Loading Level, using theoretical loading holdup and actual passive holdup

# If dryer is overloaded, load is set to 1.


load = m_p/m_load;

ELSE

load = 1;

END

U = 1 - load;

# Calculation of mass averaged fall time and height

IF load > 0 THEN

maft = 0.535877216576409 + 0.00457856290776704*phi -0.000129598737028669*(phi^2) +

1.07883836331524E-06*(phi^3) + 0.117473908470856*U -0.0744009282461775*(U^2) +

0.0810434707665877*(U^3) + 0.0128083149957092*phi*U -

263

0.00875061991473558*phi*(U^2)-0.000108364812479778*(phi^2)*U + 4.74471791775954E-

05*(phi^2)*(U^2);

mafh = 0.5*9.81*(maft^2);

tpas = acos(1-((mafh*cos(theta*pi/180))^2)/(2*(R^2)))/(omega*2*pi/60);

k_2 = 1/tpas;

ELSE

maft = 0;

mafh = 0;

tpas = 0;

k_2 = 0;

END

c1 = mafh*sin (theta*pi/180)/(L2/N2); # Geometric axial advance of solids w/o drag

264

Geometric modelling for section C

PARAMETER










VARIABLE










psi_ft AS no_unit # Angle between flight tip and flight base from centre of

dryer

265


k_2 AS no_unit





pi AS no_unit # Pi


m_bak AS mass

m_des AS mass


STREAM




EQUATION

pi = 3.141592654;







266



# Design load calculation

m_bak = rhob*dl*(-4.6584030831466 + 0.646205724290255*phi-0.0358998918593869*(phi^2)

+ 0.00106187909781541*(phi^3) -1.74218037964184E-05*(phi^4) + 1.50728281484852E-

07*(phi^5) -5.36928902950201E-10*(phi^6));

m_des = (1.24*m_bak);

m_load = m_des;




load = m_p/m_load;

ELSE

load = 1;

END

U = 1 - load;


IF load > 0 THEN

maft = 0.455364714961433 + 0.00500606517559277*phi -0.000135762841787734*(phi^2) +

1.2918647217012E-06*(phi^3) + 0.0104733203115757*U + 0.0148187169761513*(U^2) +

0.0522743789468905*(U^3) + 0.0160364376692996*phi*U -0.00896672863768799*phi*(U^2)

-0.000151022103693776*(phi^2)*U + 6.46798505794521E-05*(phi^2)*(U^2);

mafh = 0.5*9.81*(maft^2);

267


k_2 = 1/tpas;

ELSE

maft = 0;

mafh = 0;

tpas = 0;

k_2 = 0;

END

c1 = mafh*sin(theta*pi/180)/(L3/N3); # Geometric axial advance of solids w/o drag

268

Geometric modelling for section D

PARAMETER










VARIABLE










psi_ft AS no_unit # Angle between flight tip and flight base from centre of dryer


269

k_2 AS no_unit





pi AS no_unit # Pi


m_bak AS mass #design load

m_des AS mass # modified design load


STREAM




EQUATION

pi = 3.141592654;








270


# Calculating THeoretical Loading Mass using Porter's Assumption

#m_load = mf_max * Nf_4/2;

m_bak = rhob*dl*(5.91313117986886 -0.796114307860833*phi +

0.0456776806338413*(phi^2) -0.00137025615939124*(phi^3) + 2.28826870054856E-

05*(phi^4) -2.01534907281941E-07*(phi^5) + 7.31905932620977E-10*(phi^6));

m_des = (1.24*m_bak);

m_load = m_des;




load = m_p/m_load;

ELSE

load = 1;

END

U = 1 - load;


IF load > 0 THEN

maft = 0.563922134596396 + 0.00419981685959669*phi -0.000122322728935087*(phi^2) +

9.82402884711769E-07*(phi^3) + 0.155664820234961*U -0.124796430711285*(U^2) +

0.101432837793894*(U^3) + 0.0117097541137809*phi*U -0.00852018863838566*phi*(U^2)

-9.63187980449476E-05*(phi^2)*U + 4.14518306346423E-05*(phi^2)*(U^2);

mafh = 0.5*9.81*(maft^2);

271


k_2 = 1/tpas;

ELSE

maft = 0;

mafh = 0;

tpas = 0;

k_2 = 0;

END

c1 = mafh*sin(theta*pi/180)/(L4/N4); # Geometric axial advance of solids w/o drag

272

Mixing cell

{The mixing cell combines the output from the last passive and active cells in Section D. this

#serves as input data into last unflighted section}

PARAMETER


Cp_z AS REAL # specifice heat capacity of zinc

VARIABLE

F_p AS Mass_flowrate # Flowrate from the passive cell

F_x AS Mass_flowrate # Flowrate from the active cell(axial)

T_p AS mass_Fraction # Tracer conc

F_t AS mass_flowrate # Total flow into the plug section (agglomeration)

T_x AS mass_Fraction # Tracer conc.(from the active phase(axial)

T_t AS mass_Fraction # Total tracer conc. into the last plug section

x_x AS mass_Fraction # Moisture content.(from the active phase(axial)

x_t AS mass_Fraction #Total moisture content into the last plug section

x_p AS mass_Fraction #Moisture content from the passive cell

tt AS temperature #temperature into the plug section(agglomeration)

tp AS temperature #temperature of the passive phase

tx AS temperature #temperature of the active phase(axial

STREAM

Passive :F_p,T_p,x_p,tp AS SOLIDFLOW

Axial :F_x,T_x, x_x,tx AS SOLIDFLOW

Out :F_t,T_t, x_t,tt AS SOLIDFLOW

273

EQUATION

F_t = F_p + F_x;

(T_t * F_t) = (F_p * T_p) + (F_x*T_x);

(x_t * F_t) = (F_p * x_p) + (F_x*x_x);

F_t*(((1-x_t)* Cp_z*tt)+ (x_t*Cp_w*tt)) = F_p*(((1-x_p)* Cp_z*tp )+ (x_p*Cp_w*tp)) +

F_x*(((1-x_x)* Cp_z*tx )+ (x_p*Cp_w*tx));

274

UNIT

A AS Active_Phase

G AS Geometry1

P AS Passive_Phase

AIR AS Air_phase

EQUATION

P.Active IS A.Active;

P.Return IS A.Return;

P.DataOut IS G.Data_In;

P.DataIn IS G.Data_P;

A.Data IS G.Data_A;

AIR.Evaporation IS A.Evaporation;

A.Air IS AIR.Air_out;

A.Convection IS AIR.Convection;

A.masstransfer IS AIR.masstransfer;

A.Radiation IS AIR.radiation;

275

Parameter estimation

ESTIMATE

D.C1.u

0.015 0.01 0.017

ESTIMATE

D.y

0.0001 0 0.01

MEASURE

D.O.T_ppm

CONSTANT_RELATIVE_VARIANCE

(0.05:0.01:100)

RUNS

Clean

276

Experimental entity

INTERVALS

3

1500.0

60.0

2500.0

PIECEWISE_CONSTANT

D.C1.T_k_in

0.0

1.255E-4

0.0

MEASURE

D.O.T_ppm

2190.0 1.24

2220.0 1.09

2250.0 3.26

2280.0 7.38

2310.0 13.5

2340.0 31.5

2370.0 28.4

2400.0 38.4

2430.0 51.7

2460.0 40.7

277

2490.0 13.6

2520.0 10.4

2550.0 5.09

2580.0 3.49

2610.0 1.55

2640.0 1.9

2670.0 1.24

2700.0 0.869

2760.0 0.839

2880.0 0.813

3000.0 0.81

3300.0 0.677

3600.0 0.613

3900.0 0.603

4200.0 0.511

Documents

Multiscale modelling of industrial flighted rotary dryers · Title: Multiscale modelling of industrial flighted rotary dryers Author: Olukayode Oludamilola Ajayi Created Date: 12/12/2012